Hello,
I'm Fengi, and ya know, I'm new to guide writing, and any feedback is welcome! Please drop a comment, tell me what you liked, what you didn't like, and hopefully a thumbs up will follow. I'll try to take all feedback I get into account in improving this guide.
Thanks,
-Fengi

((And yes, I do have a tendency to make jokes, if you don't like it then sorry -.-))

Hey guys. I've split the guide up into two parts. The first part is the main part of the guide. It is my usual Veigar build, designed completely for damage, with at least a decent chance to survive the teamfights. It is explained throughout the guide. On the other hand, the guide listed in "Alternative Build" is designed for a more survivability based Veigar, while still capable of doing great damage. I warn you though, the alternative guide is still in beta, and I am still working on it. Any feedback is welcome!

PROS
~ Hey, I just met you, and this is craaazy, but here's my combo, so penta maybe? (He nukes.)
~ AP from his Q
~ Insanely strong combo
~ An awesome passive (In my opinion)
~ Easy farming


Cons
~ Squishy. 'Nuff said.
~ Can pretty much get 1 combo off in a team fight
~ Mana hungry early game
~ Often focused late game
~ Stun is awkward to land and takes skill
~ Requires good laning phase


((Yes, a lot of cons compared to pros, but stick with me!))

Will update soon

Will update soon

Viable Summoner Spells:

The uses for flash are awesome. Escape, chase, steal baron, escape baron...

Another versatile spell. It can be used for ganking (Teleporting to wards), getting back to lane to get more Q farm, I've even used it to escape. (Long story short, they were faster than me, so I threw down my stun and tp'd out of there.)

An awesome spell. Good for finishing off early game, and killing their adc late game when they have a ton of life steal.
Other viable, but not preferred summoner spells:

Clarity: If you have problems with mana, grab it and save yourself the trouble, though the early Tear of the Goddess usually takes care of the problems.

Cleanse: If the enemy has a team packed with Crowd Control (Slows, stuns, fears, that kind of stuff), then grab it.

Exhaust: Useful, but why are you chasing them when you're combo does all their health?

Heal: If you have problems with being too squishy, then grab it.

Not viable Summoner Spells:

Clairvoyance - You're not a support. You don't need it.

Fortify - Again, not a support. You don't need it.

Rally - Most useless spell in the game. Don't bother.

Promote - You already push fine with your AoE. You don't need this.

Revive - Revive is saying to the other team "Hey, I plan on dying alot so go ahead and kill me". You don't need to say that. Ever.

Smite - You are not a jungle. You don't get this.

Surge - I can see where some people might use this spell, but you'll already have plenty of AP. Ya don't need it.

Equilibrium (Passive) - "Veigar's mana regen is increased by 0.75% for each 1% of mana missing."
Similar to Chalice of Harmony and Athene's Unholy Grail, mana regen is increased by .75% for each 1% he is missing. Awesome late game passive, you'll almost never run out of mana.

Baleful Strike (Q) - "Active: Unleashes dark energy at target enemy, dealing magic damage. If a unit is killed, Veigar gains some Ability Power permanently."
"Passive: Veigar gains 1/2/3/4/5 Ability Power when he kills a champion from any source of damage."

Your source of early game damage. Also, one of the best passives in the game. Gaining ability power for last hitting with this ability, and gaining ability power when you kill somebody. Aweeeeeesome! Though, it has a small dropoff in damage late game when everybody starts finishing their builds, but your other abilities make up for it.

Dark Matter (W) - "Veigar calls a great mass of dark matter to fall from the sky to the target location, dealing magic damage when it lands."

An awesome Nuking ability. It has a 1:1 AP ratio, meaning that every single point of AP becomes another point of damage on this ability. Use in combination with Event Horizon for maximum effect.

Event Horizon (E) - "Veigar twists the edges of space around the target location for 3 seconds, stunning enemies who pass through the perimeter for a short duration."

Your stun. Yes, it's a tad tricky to land and takes practice. Remember, when using it, try to hit them on the edge of the stun so they actually are stunned. Your combo should follow, starting with Dark Matter.

Primordial Burst (R) - "Blasts target enemy champion, dealing a large base amount of magic damage plus 80% of his target's AP."

Your Ultimate. Absolutely decimates their AP carry. If you didn't notice, it gains bonus damage based on their AP. Absolutely scary.



Your combo:
--> --> --> -->

E --> W --> Deathfire Grasp --> Q --> R

Now, to further show it, here's a little video on veigar's combo and abilities:

Starting Items
x2

This is what I prefer to start with, since the mana regen is really helpful early phase. Usually the AP you get from Runes, Masteries, and your Q is plenty to do damage against whoever.

Doran's Ring , Boots and Health Potion x3 , or Sapphire Crystal and Health Potion x2 are all also ways to start with Veigar. I prefer the Meki pendant and health potions, but it's up to you.


Core Items

- Veigar is extremely mana hungry early game. Rushing this item helps fix that, and then later builds into an Archangel's Staff

- Veigar's best friend. This item truly completes Veigar's combo. Plus the AP and Cooldown Reduction really help Veigar. Absolutely needed.

- Your boots. The Magic Pen is awesome against those tanks early game, or even if they try getting early game magic resist. The reason I chose these over Ionian Boots of Lucidity is because the cooldown reduction is the same as on Deathfire Grasp, and they're unique passives... ((They don't stack if they're the same...))

- Rabadon's. 'Nuff said.


The Icing on the cake

- Great Armor, great active, great Ability power. Pop out your combo, pop this, and you can get your cooldowns down. Plus, it's handy for those tight situations where you're being focused. Use this, and you'll survive the team fight... hopefully.

- Large AP boost, large Mana boost, and a great item that suits veigar well.

- Pesky Pesky Peeeeesky tanks. Oh wait, *3 shot*


Other items

- I don't see too many people getting this item on Veigar. I choose to put it here because of the Health boost, the AP boost, and the slow. It's useful for chasing down those who are running, while your abilities come off of Cooldown. Late game Baleful Strike has a low cooldown, but isn't very strong. Spammable, and useful with Rylai's slow.

- Really good Cooldown Reduction, and good mana regen. I usually don't use this item, but it's viable.

- If you're getting owned by their AP carry, grab this item. The bonus Magic Resistance and AP is helpful. Plus, the passive is really a good way to help your nuking capabilities vs everyone.

- A friend recommended this to me. I found it is surprisingly useful. If you use an ability, basic attack, nother ability, basic attack, they're already dead.

- Grab it if you need some extra Magic Resist and survivability.

- Honestly, I don't get this item too much on Veigar. You've already got a zhonya's, and with it's active, you probably shouldn't die too much. It's useful, and grab it if you need extra survivability, but I don't consider it necessary on Veigar.

Early Game:
Early game just last hit with Baleful Strike. There isn't too much you can do pre-level 6, unless they're extremely aggressive. If they're getting in yo' face, then throw down an Event Horizon and then a Dark Matter and Baleful Strike combo them. Do about half of their health, and they'll back off. If they don't, keep playing them and when you get your ultimate...
FINISH THEM.
Anyways, do that and you're early game will be good. Veigar should be able to take on most champions, if not absolutely demolish them, but some characters might just be a headache.
Otherwise, just be careful against other AP nukers like Brand and Viktor, and don't be too aggressive. Remember, you're squishy. They can also nuke.

Middle game
At this point, you should have your Deathfire Grasp and boots finished, and maybe your Archangel's staff depending on how you've been farming. Teamfights will start popping up, so here's veigar's teamfight strategy:
As a fight starts to develop, pick the highest priority target. This will usually be their AD carry, or AP mid. Once you have them picked out, stun them, and UNLOAD on them. Be careful to stay behind your tank though, you're still squishy. If they're staying back and waiting, do the same. Throw a couple abilities in though. Your Event Horizon and Dark Matter is really a great teamfight combo. The AoE stun and AoE high damage ability really narrow down their health.

Late game
At this point, it's all about teamfights and pushing. You might notice a slight dropoff on your damage output as everybody finishes their builds, but it shouldn't be too huge. Keep nuking, and stick with your team. If you get caught alone, you are dead.

All in all, Veigar is an awesome character. He is extremely strong early game, and can still three shot most people. Though, don't get cocky with him. You're still squishy, but you still hit hard. Be careful, and make me proud.

Thanks for Reading,
Fengi

7/6/2012: Guide Published! Changed items slightly per nagging of my friend.
7/7/2012: Updated Item Section. Changed order of items, replaced Rylai's with Zhonya's. Updated Gameplay section. Updated Summoner spells.
12/28/2012: I'm back! I remembered this old guide and decided to update. Anyways, have fun don't hurt yourself. Changed items heavily. In process of updating runes and masteries.