Heyo! Hello summoner, my name is MegaGmat. I'm a Gold IV player that mains Veigar, which is why I chose to make a guide on him first!

My main midget man, Veigar is a great champion against most AP mids, some consider him a counter to ALL AP mids. I agree to a point. He has quite the carrying potential if played right.

This guide will be (I'm hoping) decently detailed and understandable, giving you a good idea of what Veigar is (a midget), how to play him and possibly make you see what I see. (A tiny purple spec roaming around summoners rift).

Pros:
+Strongest Nuker In-Game.
+One of the best stuns In-Game.
+(Theoretically) Infinite power!
+Good Mid-Game, Strong Late-Game.
+Makes you wonder if some enemy champions were there in the first place.
+Laugh is contagious.

Cons:
-Weak Early Game.
-Stun on long cooldown.
-Squishy.
-Small AoE damage spell.
-Usually focused on in fights.

Although the cons may seem a little harsh, it is a team game, and your team should cover your cons:
-Your weak early game? So farm. Your Baleful Strike needs to get stacked up. Keep your mana around half-point and farm your Q whenever possible.
-Your stun is on a long cooldown? Then learn to time it. Timing is key with Veigar. Your E Event Horizon is usually a death sentence late game. Know when to use it and where to use it.
-Squishy? Build some resistances and let your team tank the enemy for you. All you have to do is land stuns and nuke the enemy squishys. Sometimes just a Primordial Burst on one and Dark Matter + Baleful Strike on another is enough.
-Small AoE Damage? Focus on threats. The AoE may be small, but it CAN hit multiple targets.
-Focused in Fights? Buy a Zhonya's Hourglass or a Guardian Angel, and make sure to keep close to your team.

To win you have to know yourself, your opponent, when to fight and when to run. Know these and win the game.

Equilibrium: Basically half of the Athene's passive. Don't underestimate this. With a Doran's Ring and some good last hitting early game your mana will be back up quite quickly. Late game with an Athene's or a Seraphs, unless you spam your skills whenever they come up, you shouldn't ever run out of mana.

Baleful Strike: Your most constant source of damage and what makes veigar so scary late game. Let's look at the passive. +1 AP for last hitting small minions and monsters with it, +2 AP for last hitting large minions and monsters, and +1*(Level of Q) AP for every kill from any source of damage. You have no cap on AP, so as the game goes on, you get stronger. Stacking it is very important, so do so when you get a chance, and try to always get siege minions with it. Outside of the passive it has a ok AP scaling (%60) and short cd. Don't be afraid to use it to poke.

Dark Matter: Your second strongest spell. Huge base damage, coupled with a whopping %100 AP scaling, if this lands it WILL hurt. Although there is a downside to it, it takes 1.2 seconds to hit. So you will have to lead it or stun your enemy to get it to hit. It also reveals an area for a little while so use your Dark Matter instead of face checking a bush.

Event Horizon: Your CC. Your combo starter, your escape tool, your game changer. It's damn near impossible to land your full combo without landing this first, unless an ally lands their CC. The stun itself is a little odd compared to other champions. It's a large ring where only the walls actually stun. If caught inside they will have to run into the wall to get stunned. It has a pretty long cooldown so be careful when you place it. Most enemies will try to make use of a wasted Event Horizon.

Primordial Burst: The face-wrecker. This is a scary thing to see come chasing after you. Veigar's ultimate, along with a decent base damage, has a %120 AP scaling, and not only that, uses %80 of your enemies AP and adds that to the damage done. Late game it takes only a Primordial Burst to take out a squishy APC. Careful not to waste it though, Zhonya's Hourglass, Fizz' Playful / Trickster, Yasuo's Wind Wall can all cancel out your ultimate. A wasted Primordial Burst brings a Teemo back to life. Never forget that.

Tips:

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First off, when it comes to Veigar, things can come down to milliseconds. Meaning you need to be fast. How can you gain speed? Obviously smart cast. A surprising amount of people don't use smart cast. I can see why not to use it with some champions. Although most champions can benefit greatly from smart cast. Veigar is just one of many. Since you need to execute your combo in about ~1.5 seconds for the basic ( E > W > Q) and ~ 2 seconds for your full combo ( E > W > DFG > Q > R > Ignite) you'll need to be fast.
"But what if I can't land my Event Horizon because of its shape!?"
Well, there is a trick to it:


The thing to remember here is that Veigar's Event Horizon isn't a circle, but a pentagon. Look carefully. There are 5 corners. 4 of which are symmetrical to each other, and one that is all alone. The stun is placed according to that corner. So keep that in mind while placing it. After a few matches you gain a feel for it.

I often go with standard runes, although runes just as masteries can and should be changed according to play-style.

Against AP Mid
-3x Greater Quintessence of Ability Power
-9x Greater Mark of Magic Penetration OR 9x Greater Mark of Ability Power
-9x Greater Seal of Armor Or 4x Greater Seal of Mana Regeneration + 5x Greater Seal of Armor/5x Greater Seal of Magic Resist
-9x Greater Glyph of Magic Resist Or 9x Greater Glyph of Ability Power

Pretty standard, I don't find the mana regen runes useful after you get Chalice of Harmony or Tear of the Goddess though. I reccomend MR glyphs so you don't get bursted down too easily.

Against AD Mid
-3x Greater Quintessence of Ability Power
-9x Greater Mark of Magic Penetration OR 9x Greater Mark of Ability Power
-9x Greater Seal of Armor
-9x Greater Glyph of Ability Power OR 4x Greater Glyph of Mana Regeneration + 5x Greater Glyph of Ability Power

Also pretty standard. You may want mana regen runes so you can throw a Baleful Strike every once in a while but I'd much rather have the AP personally.

Offense
Double-Edged Sword : Once the ball starts rolling 1.5% damage is pretty big.
Sorcery: %5 CDR off the bat can help squeeze a few more Baleful Strikes to stack it up more. CDR in general is good for Veigar.
Mental Force : More power! MORE POWER! MOAR POWA! Extra AP is always good.
Arcane Mastery: 6 AP straight off the bat for a stronger beginning phase.
Executioner : %5 more damage to champions with less than %50 health.. Late game that means roughly 100-200 damage depending on the enemy. Yowza.
Archmage : %5 more AP. Why are you even questioning it?
Dangerous Game : It may not seem like much but that little bit of health and mana can mean life and death.
Devastating Strikes : %6 magic and armor pen. Add that to sorcerer`s shoes and Void Staff and ask yourself why there is dust where the enemy adc stood moments ago.
Arcane Blade : Basic attacks deal +5% of AP. Late game this makes your auto attacks do about 300 damage on turrets. Wait, what turret? What's going on here?!
Havoc : Bring the storm. No, stahp Viktor! I meant me!

Utility
Phasewalker : Have you ever gone split pushing and looked at the map to see no enemy champions there? That is possibly the truest feeling of fear. That 1 second can mean the difference between life and death. Don't underestimate it. Farming your Baleful Strike is important all game, so is a speedy get away.
Fleet of Foot: Being faster than your opponent is good to catch up to them, or run away from them. That slight bit of speed can mean a successful stun and kill, or a smooth get away.
Meditation : Mana Regen. 'Nuff said.
Alchemist : Turning minions into gold is a hard process. Even harder when it comes to champions. A teensy bit more health and mana might save you from an ignite, or let you back into a fight.
Culinary Master : Potions might taste awful, why submit yourself to that? Instant 20 health and 10 mana is huge early game. At level 2 ignite does 90 damage. Just saying.

You can go with the classic 21/9/0 mastery page but Veigar is a Burst champion, he's not built to survive a lot of damage, he's built to put out a lot of damage. In the laning phase I find this set up gives you better sustain. If you're unsure of yourself, or think the defence page might be better against your opponent, go for it. You and I are most likely nothing alike. Personal playstyle and preference is much more important. These are just guide lines that I advise. If you don't wanna listen to them fine.. whatever.. I don't care.. *sob*

Doran's Ring: Great stats and good starting item against most mids. If you feel comfortable in your abilities to stay alive, I reccomend getting this first.

Rabadon's Deathcap: One of your 3 (big) best friends. Between your items and your Baleful Strike stacks the amount of extra AP this gives is astonishing.

Deathfire Grasp: Most likely your bestest friend out of your 3 best friends. CDR, AP, %20 more magic damage for 4 seconds, its got it ALL. Using this item in your combo (E > w > DFG > Q > R) will most likely gaurantee you the kill depending on the enemy, the phase of the game, and your AP.

Zhonya's Hourglass: Your last, but definitely not least, best friend. Decent resistance, large amount of AP, and an active to protect you against all the hatred in the world (for 2.5 seconds every 90 seconds), it's a supportive type of friend. Even if the enemy team doesn't have any AD assassians, it can be worth picking up.

Void Staff: Magic Resistance? You cannot resist my POWER! *Evil laugh* This is a must have on any build. You're a nuker. Meaning you have to be able to put out as much damage as possible in the shortest amount of time. Destroying any resistance in your way is crucial.

Sorcerer's Shoes: Oh I see you bought a negatron cloak. It'd be a shame if someone were to.. CUT STRAIGHT THROUGH IT! (I did think of using a different term than cut) One of the only 2 worthwhile items to buy that have some Magic Pen on them. They make you hurt a LOT more.

Seraph's Embrace: Stacking while your stacking eh? You should stop watching so many movies. Seraphs Embrace is a great item - +1000 mana cap, 60 ap + (+3% max mana), and a shield that protects you for %20 of your current mana. Yup. It's just that awesome. It's a good item if the team fights are long and the enemies like to focus you. Coupled with a Zhonya's Hourglass your pretty darn hard to kill. Kind of.

Athene's Unholy Grail: You have a Baleful Strike! And you have a Baleful Strike! Everyone get's a Baleful Strike! Did you know Veigar's middle name was Oprah? Yup. The %20 CDR and passive make Athene's very worthwhile getting. %90 of the time you'll want to get it, even if your lane opponent is AD. In that case just buying the chalice until further need will suffice.

Stealth Ward: You're a mid laner, not a jungler. The sweeper has very little use to you. Ward coverage is more important. Since you only have 2 options in trinkets, *wink*, you should always get the Stealth Ward.

Items outside of these are extremely unnecessary. The ONLY item I can see working outside of the ones listed above is Lich Bane. Veigar is a BURST champion. I cannot stress that enough. However in the off chance that the game goes beyond the 60 minute mark, a Lich Bane could prove to be useful. If I see you walking around the rift with a Rylai's Crystal Scepter you can be expecting a Dark Matter on your head.

Explanations Below

Take Flash and Ignite.
You may want to take Barrier, Cleanse, Heal or Teleport.
I will find you and make you refund Veigar if you use Ghost, Clairvoyance, Smite, or Clarity.

Exhaust and Revive are in a Grey-Zone.

Flash: Your best way of getting out of a sticky situation.
Ignite: A good way to finish off your combo (along with an auto attack or two)
Barrier: If the enemy is really bursty (e.g Syndra)
Cleanse: Against a team with a lot of CC or someone like Zed to cleanse his Death Mark.
Heal: After the update seems to be better than barrier. Best way to find out is to test.
Teleport: Getting into a fight is important. Even if you're behind a well placed stun can land your team a kill (or several).
Ghost: You can hide but you can't run. Seriously.
Clairvoyance: Don't even get me started.
Smite: You're playing Veigar not Nasus (A.K.A Susan) don't imagine jungling.
Clarity: You won't EVER need it. EVER.

Exhaust and Revive: I can see why you may want to take either. As a VIP Revive can help get you back in the fight, but you may not always be a VIP. Exhaust may be good against someone like Syndra with low mobility and high damage output so you can get away. But in a proper 1v1 you should be able to take her out. I don't really reccomend either, but I can't say don't EVER use them either.

I'm not quite sure you can call it a 1 person wombo combo, but I think it's a better way of disintegration than Vel'Koz' Life Form Disintegration Ray. Just saying.

Pre-6, around level 3-4 you may want to just do a simple combo to show them who's boss.
A simple E > W > Q should do the trick. If you find the chance to do it again before they back or use potions to get back up, another one of these + Ignite should get a kill.

Post-6 I like doing a E > W > Q to lower my enemies health and then do a E > W > Q > R + ignite. Against AP champions that's a %95 kill. Sometimes you won't even need ignite. Against Ad champions.. You may wanna throw a q in between combos.

And lastly Post-DFG. After you get Deathfire Grasp you wanna use it after you use Dark Matter and before you use Baleful Strike. So it should be something like E > W > DFG > Q > R + Ignite. Mid Game this wrecks most champions. Not always guaranteeing a kill but almost always getting them out of the fight.

Late Game you'll most likely wanna q > r the apc on their team, netting another kill. If you get the chance a e > w > q + ignite should kill an adc during this phase of the game, but if you really wanna make sure add your ultimate.

Difficulty will be shown by color of Champion Name ranging from Green to Yellow (light) to Yellow (Dark) to Red (easy - easy-medium - medium-hard - hard)

Ahri: The famous foxy lady. She's somewhat similiar to Veigar. She needs to hit her CC ( Charm) to pull off her combo perfectly. Although there are some pretty big differences. Her CC can't pass through minions, it's shorter, she isn't as strong late game as you (but then again who is?). A tip for Ahri is to wait for her to use her ultimate ( Spirit Rush) stupidly. Her ult is a dash, so if she does that through your Event Horizon she WILL get stunned. Anyone want cooked fox?

Akali: Akali is nothing without her Shadow Dance. If you can force a kill out of her pre-6 you should be able to assert dominance in-lane and snowball from there. Most Akali's build a decent amount of AP so bursting her shouldn't be too hard. Just be careful about how you place your Event Horizon, and if she gets in your face using it on yourself is your best bet.

Annie: The Fire Child. Darkness vs darkness. Annie is an interesting champion. She has decent mana sustain with her Disintegrate's passive, her cooldowns are relatively low, and she has one of the best stuns in the game. Worst of all, her stun can be both single target and AoE, so what do you do? You play the skill game. This lane is a skill match-up, the first to land their stun will win. She can poke you more freely early game so be wary not to get close to her. Just make sure you stun her before you go in all game long.

Brand: This man is on FIRRRRRREEE! He's walking on FIRRRRRREEE! Brand is rediculously strong. However his CC ( Sear and his Pillar of Flame are both skill shots, with his CC being a conditional skill shot mind you. Early boots are important in this lane. Like Annie, if he catches you, he'll make you midget toast.

Diana: Similiar to Akali, but so very different. She's a champion you don't want to get close to, but since she's melee, you have an easy time against pre-6. Her Crescent Strike is the only thing to be cautious about until then. Not too hard to dodge though. Just make sure you don't get hit by it or she gets a free Lunar Rush proq on you. And it hurts. Her ult is also a dash so she can get stunned if you time it just right.

Fizz: Something smells.. fishy. Fizz if played correctly can counter you to high heaven. What the heck did I just say?.. Anyways his kit is perfect against you - a gap closer ( Urchin Strike, a damage over time aa boost( Seastone Trident, and a skill dodge( Playful / Trickster). The first 1-2 levels you have an advantage so poke at him while you can, like when he goes to farm. Once he gets his Playful / Trickster he can use that to go through your Event Horizon messing up your combo. The only way to win against him is to wait for him to use his Playful / Trickster. Post-6 he'll most likely do an r ( Chum the Waters) > e ( Playful / Trickster) > q ( Urchin Strike) combo, so you'll have to stun him when he gets out of his Playful / Trickster. Play safe.

Gragas: After the update Gragas became tankier. He still has some good damage but not quite what he use to be. Now he's much harder to burst. He'll likely build some MR against you. A lot of it. An early Void Staff may help in this fight.

Katarina: Nope. Just nope. No no no no no no no. This matchup is a death match. Her Shunpo is a blink so unless you land your stun right on her, you won't be stunning her. Her Death Lotus does a lot of damage in a short period of time and she'll most likely buy an Abyssal Mask to counter-act your damage. Unless your jungler helps stay under turret.

LeBlanc: Now you see her, now there are.. 2 of her? Wrong trick bro! LeBlanc has 2 things that make her difficult: a good gap closer ( Distortion), and a 2-stage silence ( sigil of silence). The thing is she has 3.5 seconds to proq that silence. That's a decent amount of time. Most LB's will Distortion after sigil of silence to silence you and then use Ethereal Chains to stun you. The thing is the first stage of her Distortion? It's a dash. You CAN stun her. Although the second stage is a blink, so no go. Just watch out for her silence and make sure you don't waste your [primordial burst on her passive Mirror Image. Remember, wasted ult = revived Teemo. You don't wanna do it. Make sure you ult her before she gets to that point, unless she has a buff on her.

Lux: Your polar opposite. The lady of light. Veigar doesn't like her. You shouldn't either. Her skills aren't hard to dodge, however are highly rewarding for Lux if they do land. You'll want to make sure you don't get snared, otherwise she can and WILL burst you down. Some lux-y ladies like to Final Spark blue if they see you've gone to it. Make sure to pull it to the side so it doesn't get stolen.

Nidalee: Me-OW! The bad kitty of the forest. A sustainer with a huge powerspike at 6. You'll want to get a kill pre-6 or keep your distance post-6. Make sure not to push to her tower post-6 since her gap closer ([pounce]]) is on a very short cd. Dodge her javalin toss' and ping when she's gone. Should be easy to combo her once she gets some ap going.

Ryze: Nope. I don't wanna go to mid lane! I wanna fight Tryndamere up top! Ryze is one of your strongest counters. He is nearly impossible to 1v1 post-6 and doesn't need to build AP to be strong. He will make you cry with his damage and strong defence. Shut him down early or stall till late. Ryze falls off hard in the late game.

Syndra: May the balls be ever in your flavor. Favor. Shut up. The pokemon master, the juggler, the dark witch of the north. Syndra is similiar to Veigar. Bursty, slow, powerful. However her 3 main skills are all skill shots. If you can keep your health up until 6, you should be able to burst her easily.

Ziggs: Yordle vs Yordle. Poke vs Burst. This is it ladies and gentlemen. Ziggs is painful in several ways. He has a slow, high damage, and an odd form of CC ( Satchel Charge). The thing to remember is that all the minions are your enemy. Stay away from your minions. The AoE of his abilities are annoying, but should be easy to dodge without something to take the hit. Post-6 Ziggs doesn't stand a chance.

Zed: Oh.. Hi.. Zed, my buddy, we both like darkness, why can't we be friends? Please? Zed has several advantages over you - he's AD, that's a giant slap in the face, he has a blink, he has medium and close range damage, and he's an asassian. All game long he will be your foe. Like Katarina the only way to beat him is to land your stun on point, or wait for him to waste his Living Shadow. Although a jungler's help is always good.

Thanks for reading my Veigar Guide. It's not quite as comprehensive as I'd like, yet. I'll work on it more as I find the chance. This is my first guide. So I hope you don't go too hard on me, although constructive criticism is always welcome. Please upvote, give me feedback and suggestions.

Good luck bursting down your foes.
*"Evil" Veigar Laugh*