Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
This build is what I usually do and it hasn't let me down that much, usually 4-5X more kills to deaths.
Pretty straight forward, just select the bonus to a summoner spell that suits your play style.
I run teleport and clarity for the obvious reason, mana on a stick and get back to the fight faster after purchasing items or if a tower is in trouble. But again, like I said in masteries, you can choose whatever suits your play style.
Like any Veigar build, Baleful Strike is your bread and butter early to mid game and late games makes for a good insult kill spell to already bolsters your already impressive ability power pool. As for event horrizon and dark matter, it depends on what I'm fighting against, if there is a lot of range dark matter is a bigger priority, but if there is a lot of melee the skill pick up if reversed. Primordial blast is of course picked up whenever it comes available
I choose to use the ability power per levels one because baleful strike compensates for the lack of early game ability power, by level ten you should be sporting between 50-90 ability power without any sort of ability power items.
Usually go for the Tear first for stacking that mana early game will help in the long run and notice a bigger spike in AP when you buy archangels staff, by level 15 you will have 2000 mana and Veigars passive will pretty much make sure you never run out and if it dips lower that what you like, clarity. Now the items that make Veigar annoying, as you start building more and more AP and with Will of the Ancient prepare to be almost unkillable, if you are low on health a well placed dark matter will give back a good chunk of health back, When a dark mater that does 600-1000 damage end game, that's a lot of healing. As for the rest of the items, AP, AP and even more AP.
Playing as veigar, is simpler than you think, Cautious early game and halfway though mid (if that makes sense :P) up until you get to about 150 AP, towers/teammate damage and Event Horizon will net most of your kills, and Cautiously aggressive, let you teammates jump into the fray for you and with event horizon you will be able to prevent a decent amount of pincer attacks buying time for you/your teammates time to back track and destroy your would be "hero". Late game you will be packing enough power to drop a lot of champions to half to quarter health with just dark matter normal attack and Baleful Strike and be sure to use Primordial Burst as a starter to kill a hero, that 3-5 AP is too good to pass up. Master stunning with Event Horizon and you will be on your way to annoying the less skilled and skilled a like.