Poke down your enemy until you are SURE they will die under your spell rotation. Play passively unless an opportunity comes up, poke with Q occasionally while farming, and autoattack for poke also. Pre level 6, avoid using Q just for poking, last hit a minion with it and poke the enemy simultaneously.
For me, I poke the enemy down to ~700 health and then I go all in with EWRQ, if they have high MR, throw in an ignite
Veigar is extremely weak early game, so you must be very careful. Late-mid game is Veigar's prime.
Veigar is actually a weak champion at high elo, because players know how to deal with him. However, at our level, they don't know how and just call Veigar op >.< Sustained damage people have been stupid enough to keep fighting me after I failed a rotation on them.... allowing me to autoattack them or Q them to death >.<