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.
If you farm right you will end up with an ability power around 800 without baron buff or elixer of brilliance. I pick baleful strike as first skill, it deals damage and if it kills its target you gain 1 ability power permanent. Tear of the goddes makes your mana pool big, and fiendish codex, veigar have long cooldowns, so the cooldown reduction is a must, besides it gives some mana regen. Lichbane not only gives you mana and ability power it increase you movement speed and everytime you cast a spell, you get your ability power in bonus to your next attack (it has a 3 sec cooldown)
Ignite is not a must, just pick it for the extra damage. ghost how ever is somewhat of a most, you are squishy and need the movement speed to flee if they try to gank you.
A good placed event horizon can make the whole different in teamfights, it's and aoe stun which deals no damage, but if you stun their whole team, you can get some free kills, which gives them a great disadvantage.
Remember, its okay to kill steal as veigar, because you gain permanent ability power each champion kill