Hello, welcome to my Veigar build where i'll guide you to the ways of evil with this little guy.I got the troll builds that i've tried out and they are really messed up.

The quints i picked were flat out ap because you'll need it to poke your enemy and to farm your ap with his passive.
The marks i chose were magic pen because you'll need it for late game. This guy does serious loads of damage in late game and i recommend that using magic pen runes will help you nuke more enemies.
For seals i chose flat out armor, it helps you in game because of how bloody squishy you are so you'll need it.
For glyphs i chose ap per level because it gives so much ap and you'll be needing a lot of ap for this guy to work his magic!

Use the ap runes for all my builds.

AP VEIGAR
Veigar is the boss at farming. His q's passive is really good to farm that ap you need for late game. You should start killing enemy champions by level 9 because your q will be maxed out and you gain a permanent 5 AP FOR THAT KILL. Be wise and don;t spam your q because this guy gets really mana thirsty early game.

AD VEIGAR
Keep attacking minions till pretty low and then use your q to finish them off to get your ap. At level 9 use your abilities except your stun on the enemy and when they're nearly down stun and finish with auto attacks.

AP troll
Keep farming for the build. Archangels stack, so yea. YOULL have 1000 ap.

Veigar's stun was made very good that it'll force enemies to flash out of it or stay in his circle of DEATH. His stun can initiate or turn around a teamfight and the stun is for 4.5 seconds when maxed out. Thats really good. Its good enough for your team to kill their whole team.

So remember, this guy is really good.