First of all I want to say that this is my first build made here. Also I want to admit that I am not from Engliish speaking country so sry for some grammar etc.

I dont think there is something to say about runes. You can see I choosed more ap runes to max the bonus in early laning and to make easier to lasthit creeps with your Q. You can also choose cdr seals in stead of ap seals.

For Masteries I choosed the classic caster build 9-0-21 maxing mana regen in utillity coz veigar is hell mana eater early and mid game.

Pros:
-huge nuke dmg
-AOE stun
Cons
-no gtfo ability( only stun but it has a long CD)
-squishy
-mana eater early game

The summoner spells I like to play veigar are Teleport and Flash.
I am using teleport to go fast recover mana/hp while early game and quick back to mid.
Other usable summ spells that could be used are clarity(which is kinda useless lategame); then ghost,ignite and other classic summoner spell that can't be bad to use :)

Farming is one of the most important thing that u have to know with veigar. If u really want to own you have to kill as much as possible creeps with ur Q abbility to max ur AP. also it is pretty nice to lasthit creeps with ur autoattack when Q is on CD.
WARNING!!!: DO NOT USE METEOR AND STUN TO FARM AT EARLY GAME!!!..... it will cost u so much mana so no meteor until u are sure it will not eat ur whole mana :)

In early game u focus only on farming creeps and lasthiting them with Q.Also try not to be hit by enemy champ. also try to stun them if they are in range of the turret and the turret is attacking.

This is the part when u have ur Lucky pick and maybe Fiendish Codex or If u farmed well Deathfire Grasp. Here is ur time to rape them all down :) but there is some rules.
1.u have to land ur stun If you dont the action is screwed up :(
2. If u did ur stun good then aim the meteor a bit behind the target if it would run.
3. get him what he desires hit ur Q,R and Deathfire
4. Gj veigar :)

by this time u should be really feeded :)
STAY BEHIND UR TANK!!! dont forget that u are squishy and maybe first target if ur enemies have some piece of brain :)
the thing is pretty same as in the mid game just that u will start with deathfire Grasp so it will look like this
1.Stun
2.Meteor + Deathfire
3.Q,R
4.kill the others that survived with Q
5.Gj veigar.

At the end I want to thank to all who red this quide. I hope it was helpfull and I want to hear some feedback so I can get better next time :)