Hello !
First of all, before starting this build I would like to apology for my bad english, since I'm french, and invite you to feel free to correct some big faults you may see troughout this build.

That said, I wanted for long to make a build on Mobafire, and so here I am ! This is my first build, and I make it on one of my favorite champs : Veigar.
This champ is so amazing cause of many thinks : farm easily, two AoE spells, freaking huge nuke on his ultimate. Well, he has plenty of qualities, and is a true nuker, especially against mages, which Veigar can couter really easily : I often kill the AP carry of the oppenent team in just two shots ! That's so amazing !

So I made this build in order to share my way of building the Tiny master of Evil, and to get comments on how should I get better playing with him. I hope it can help some of you too.

Ha yeah I forgot : the item build you saw before is just a build for when the game goes on perfectly, and I did not show the path in it. I'll develop it in the 'Items' section, go there for more detail

Here we go !

Pros :
-Amazing nuker
-Easy farm early game on
-Can gain AP while farming
-"Anti AP char" ultimate
-AoE Stun
-AoE nuke

Cons :
-A passive that does not really help early game, when you might have mana problems
-Might be focused quickly
-Squishy

I think the mastery are self-explanatory. Veigar is an AP nuker, so we pick 9/0/21. In the utility tree, we pick mana regen cause it'll be easier to farm early game on like this.

Ignite
Ignite is an awesome skill cause you have a little more nuke, which you can use when your other skills are on CD. It is useful against champ who can heal themselves too, such as Dr. Mundo, Tryndamere and many others.
However you can pick Ghost for escaping or chasing, Exhaust for another crowd control spell, or Teleport to go back really quickly to your lane.

Flash
I think Flash is a must on Veigar. You can Flash out of a bush, stun and nuke with all your might, chase, escape... This summoner spell is versatile and can give you great possibilities of placement during a teamfight.

Ok so now, we'll look at the runes.
Greater Mark of Magic Penetrationis just natural.
Greater Seal of ReplenishmentOk, here is the point : early on you want to farm as much as possible with your Q and you won't really focus on doing ganks or getting kills. So you will need MP/5 cause you will use your Q really often, and it will cost much mana. I pick flat MP/5 cause it's better early on, and as soon as you have Doran Ring + Tear of the godess you won't have any problems with your mana anymore.
Greater Glyph of Scaling Cooldown ReductionYou get 9% CDR with your masteries. With these runes you have another 8%. With Deathfire Graspit's another 15%, so a total 32%. With an elixir (or Mejai if you have 20 stacks) you have your CDR caped.
Greater Quintessence of Magic PenetrationJust a preference, you can use Greater Quintessence of Ability Powerinstead so farming will be easier.

Baleful Strike
Baleful Strike is your main farming skill. You get 1 AP point every time you kill a minion or neutral monster, and X AP point everytime you kill a champ (X is the level Baleful Strike is at)

Dark Matter
Dark Matter is an AoE spell with a huge nuke. With it you can destroy a minion wave in one hit, or harass pretty well if you know how to use it.
Here's a tool on how to make sure your Dark Matter will land on an ennemy champ : when you use your stun, you have two ways to it your opponent with Dark Matter : using it on the ennemy as soon as he is stunned (if you are a bit late he will go away before Dark Matter will fall), or if you are late you can use it on where he will most likely go. Most of the time he will be hit, or if he notices it he will be stopped here and you will be able to catch up with him, or will go near you. At that time you can launch Baleful Strike.
However some champ can escape this, such as Katarinawho can Shunpo to the other side, without being hit by Dark Matter, or Tryndamere, that can escape it too if he knows how to play.
It can also be used as a ward when you want to go into a bush. Pop Dark Matter into the bush, and you will be able to see what's into it for a moment.

Event Horizon
An amazing AoE stun ! If your ennemies goes trough it they are stunned for 1.5 to 2.5 seconds ! Or if they don't want to be stunned they can run into the inside of this spell, but they can't flee ! Even if they try to flash out they'll be stunned a bit farther !
However I don't recall well cause I last played Veig like 1 week ago and I'm not sure, but I think Katarina can shunpo out of it without being stunned, if someone can confirm it?
Also, by putting the limit of the AoE ON the champ you target, he'll be stunned directly, and won't have to pass trough the limit of the zone to be stun.

Primordial Burst
What can I say? The most amazing anti AP carry skill in the game !
At level 3, 500(+120% of your ability power)(+80% of the opponent ability power) damage ! With this you can kill an AP carry in two spells ! If you have an AP carry on your lane, cheers ! At 6 it's an easy kill !

Here is the skill sequence :


I max Baleful Strikefirst so it's easier to farm with it, and it becomes easier to get extra AP. Also, when you kill a champ, you gain more AP as it level up.
Then I max Dark Matterto have a better nuke.
Putting a point in Primordial Burstas soon as you can is self explanatory.

While playing with Veigar you'll try to get as much AP as possible, while maxing your CDR and having some Magic Pen.

As many of you know, when playing, one should have a core build with the champ he's playing, composed of 3 or 4 items he'll buy in all of his game, without exception. The free slots are used to buy situational items. Your core build with Veigar should look like that :
Sorcerer's Shoes Mejai's Soulstealer Archangel's Staff Rabadon's Deathcap

However, you can replace Mejai if you don't like that item or if you fail getting stacks (with a Void Staff, maybe?)

The rest is up to you. The ideal ending build is the one you saw before, under the skill sequence, for a game when you're fed and you know that people don't focus you, which will never happen at high ELO.

If you face a fed AD carry, get a Frozen Heart which will give you the CD you need, more mana and so more AP with Archangel's Staff passive.
If you have to face many CCs and nukers, get a Banshee's Veil, more AP with Archangel's Staff, more survavibility, an amazing passive, a nice MR.
There is many other exemples, but I won't quote them all.

The only 'path' I follow for buying my items is a small path early game on, after that I buy items following what I need at the moment.

Early game Path
At first I buy a Doran's Ring to have increased survavibility, some MP/5 and some AP before going to my lane.
Then I buy Boots and Tear of the Goddess on my first trip back, or if I can't afford it I buy at least boots and Meki Pendant.
Then, after finishing my Tear of the Goddess, I finish my Sorcerer's Boots, and start building depending on who I face and what I need.

Just a tip to increase your nuke early one : I often pick Haunting Guise. Early game on, it gives you like 5x M.Pen, and so a huge nuke, cause often the M.Resist item are picked end game by other carries. You can go and slaughter them now.

First of all, you should choose which lane you will go on. I always try to pick mid. Why? It's simple : the farming is easier and you will stack AP in no time if you're good, as well as gold. Also, at level 6, when you'll try to get kill, since the opponent is alone, no one will try to disturb you.
However, if you can't have mid, it's not really a problem, just be a bit more cautious when you farm, and when trying to get a kill. Also, try to have your team support go with you (that way you will most likely pick the kills you need, since the support doesn't need them, and if he picked Clarityyou will be pleased)

So, before 6, you should only be focusing on farming, with your Q of course, so you can stack AP, without any items. If you can afford it (in mana terms), you could try to harass your opponents with Dark Matter, but never with Baleful Strike, which you are keeping for farming.

At 6, back and get your boots as well as a Meki Pendant. Tell your buddy to let the opponent push, and try to get them by surprise. Use Flashto go in (if it's available), drop Event Horizon, Dark Matter and finish the carry or the squishy with Baleful Strike and Primordial Burst. If you can keep one of those two last skills to finish off the second guy you have on your lane (if you're not mid) with it and Ignite, do so.

Once you did this, focus again on farming until your ult is back. Then gank again. Keep it on until the laning phase ends.

Your role in teamfight is really simple : just put a stun around as many ennemies as you can, and then focus their AP carry. Often the Baleful Strike+ Primordial Burstcombo will be sufficient to take down this guy, and so you will be able to drop Dark Matteron the others.
Use Baleful Strikeas soon as it's available (with your CDR caped and level 5 on the skill, it has a 2.4 seconds CD)

Many of you must know what SmartCast is already, but I will explain it here : basically, it allows you to play all your skills as Karthus's Lay Waste. You just have to click on the area you want your skill to land, and it will land. For skills which need a target to launch, put your cursor on the target and launch the skill !

Smartcast is a great tool to play with, cause it will be able to launch a skill with only one step (launching the skill), meanwhile when you don't use it, you have to launch the skill then confirm the target. So, using smartcast you'll launch your spells quicker.

I think it's good to play Smartcast at least on Baleful Strike and Primordial Burst, and on your summoner spells as well.
On AoE spells it's a bit harder cause the middle of the AoE will land on where you launched the spell. So to launch it correctly you have to perfectly know the range of your skill. It's harder, but you can use it too.

Well, I believe that's all ! I hope you enjoyed this guide and that it wasn't too bad !
I hope you understood me too, and that it will allow you to understand how you should play Veigar.
Don't forget that the build can be changed ! It's just a base for playing this hero, you can adapt it to create YOUR style of Veigar !
Also, keep in mind that you're not playing 1v5, that LoL is an amazing teamgame with a lot of possibilities, and it'll be allright.

Have fun playing !