Veigar is a ranged mage which involves tons of damage in late game.

For items take Doran's Ring as first item for a better farming technique using Q's passive to get more Ap,this type of farm will also help u with Archangel's Staff which will give you bonus mana and AP,giving Deathfire Grasp a very large amount of power over hitting a opponent.
Try to last hit minions and champions with your Q skill to receive a bonus AP that is very helpful for Veigar,making him one of the most OP champions on the mid.
Veigar has also a combo use your to trap your enemy,the use your W to hit the enemy,but be careful about the next move of your opponent.
If you are ganked,always keep some mana for the E skill,stunning the enemy and breaking free.
In 3x3 invest your first point for the E skill to stun the enemies and get the first blood.
Never use your W to farm unless this spell can kill a minion by one shot.
Maximize your Q for good farm,then your E to stun the enemies for a longer period,then your Dark Matter for a bonus damage :D.