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.
Summary] How i started this was first by getting more speed and attack speed by getting the berserker's greaves. That was my first item built. I did this so i can farm more and try to get more minion kills. Also want to pick Baleful Strike as your first ability, so you can last hit minions to up your ability power. Towards the end of the game Veigar should have an balls amount of abilty. So after you get the Berserker's Greaves your gunna want to go for the scepter, cause this will give you some more health to work with. When you do this at this time you should have your ultimate ready, but Veigars ultimate has about a 130 second cooldown, but with the items i have listed you can cut that down to about 65 seconds which is really good. The main people your gunna want to try to get into battles with are champions that have high ability power cause he will be dishing out unholy amounts of damage to them.
Spells: I picked Ghost and Clarity cause ghost is very helpful for running away and also chasing people that are almost dead, but you don't want to over-extend yourself when you are chasing. So you have to be smart when you turn ghost into and offensive spell. I use it mostly for defense for running away. Then i picked Clarity cause it helps alot in early game for Veigar cause early game you will be running into a sort of mana problem, so that is why i picked this. A thing that you could do to fix this problem is your first item you could buy would be meki pendant but i have never done that and i have been fine. If you really want to you can buy some mana potions just to start off. That is up to you if you want to do that.
Abilities: Baleful Strike is the first ability you should pick cause you want to last hitting minions in the beginning of the game. If you are a beginner with Veigar you might find it hard to land Dark Matter but it will take sometime. The thing you should do is try stun them with Event Horizon then use Dark Matter. What I also like to do with it is scare people off with it, cause they will know its coming (if they are a good player) by the sound and it will show on the ground. So when they go back you can push forward a little, but remember not to push to far. Event Horizon is a really good move to use first if you want to try to kill someone and it is really helpful when you have another person with you. A good partner to team a lane with would be any kind of melee dps champion. When you get your ultimate try to save it for a champion that has alot of ability power cause it will be doing balls amount of damage to them. By the end of the game your cooldown times for your abilities will be: Baleful Strike= 2 secs, Dark Matter= 7 secs, Event Horizon= 11 secs, and finally Primordial Burst= 65 to 68 secs.
Hope this helps!