Disclaimer: This obtains how I Dremu play Veigar, This is not the greatest build ever, This is how I use him and I've found it works very well.

Veigar is a great nuker mage, He is one of my favorite mages at that, if you play him right you can succeed very well with him and do tons of damage, He is AP based which means you will be best if you stack AP mainly.

Veigar is a great mage, Your most useful skill will be his, Baleful Strike You will be using this most often, This build will make it so that mana should not be a problem at all. This build takes some skill, It is not recommended for new players.

As Veigar you will be stacking AP (Ability Power), In the beginning until level 6+ you will be in the middle killing the minions with finishing each at low health with your Baleful Strike, This gives you 1+ AP PERMANENTLY per kill. This is very useful for Veigar to be a nuke mid/endgame.

Depending on your money income, Say your killing a lot of champions easily, You will follow the items list above. Or if your not getting many champions but still getting quite good gold, You should then get Sheen before the Rabadon's Hat, This will save you more money and still keep you up there.

Pros:
1. Champion Slaying
2. Quick Leveling
3. Mana efficient
4. Harasser

Cons:
1. Squishy
2. Slow
3. Easily harassed

Skills:

Equilibrium is Veigar's passive ability, this increases his mana regen for every 1% mana missing, This makes him able to cast spells a lot more for his great amount of mana. This also allows him to stack more AP dependent items then mana dependent.

Baleful Strike.
Your most useful skill, You'll spend 90% of your mana on this skill, It damages the enemy by a fair amount but also it is good for the beginning when your farming AP because the final blow with this spell on any minion will increase your AP by 1 permanently.

Dark Matter.
Dark Matter is a very powerful skill, Used in combination with Event Horizon(Below) it can be a powerful tool when destroying your enemy.

Event Horizon.
Event Horizon is Veigar's stun, You can be using this A LOT for escapes and for stopping your enemy from escaping, You can even save you teammates *I use it for 3 things basically, Saving, Escaping, Damaging. With event horizon you should always use Dark Matter for increased damage while stopping the enemy.

Primordial Burst.
Primordial Burst is your most powerful tool to destruction. At level 6 you will start your spree of champion slaying, With primordial burst it is always smart to aim at the enemy mages, This skill does damage plus adds the enemy's AP therefore it can be used to 1 shot a mage, Or do massive damage combined with other skills.

Rotation:

I've found that this spell rotation works very well as to handling the enemy quick and efficiently.

1. First your going to need to be atleast level 6+ to start ganking the enemies. When in a fight with a Champion try to be the first to attack, Throw your Baleful Strike at him to drop his health, Do this to harass the enemy as well.

2. Once you've damaged him somewhat, It is time for your Event Horizon, This will give you enough time as to stun him but from then on you must be quick.

3. Right after the even horizon use your Dark Matter right on them or a little in front, As long as they are hit headon to deal maximum damage, If needed use another Baleful Strike before step 4.

4. Finally, once their health is very low use your ultimate, Primordial Burst this ultimate is VERY useful as it uses their ability power added to 275/350/500
Depending on their AP you can easily one shot the target with maybe 1 Baleful strike to start it off, If your up against another Veigar they will be stacking AP as well, I've one shotted veigars many times from Primordial Blast.

A broken down Rotation is below:
-- Q,E,W,Q,R or E,W,Q,R,Q --
Either one works well.

So, By the end of your match you should always be the top or up there depending on how well you followed my guide, I usually do very well, Some games better than others. Veigar is a very good mage to play, Depending as to knowing what your doing with him, If it is your first time playing Veigar this will help out a lot as to getting to know him or if your skilled with mages then you should have no problem with Veigar.

I would love some

Feedback

and suggestions!

Please enjoy the carnage of Veigar :]

PLEASE SEND ME SOME PICTURES OF SUCCESS YOU'VE MADE WITH THIS BUILD AND I'LL POST IT IN MY BUILDS!