First, dodge Veigar's E as much as possible. His W relies on it, and he usually can't position safely for Q without it. Failing that, get Mercury Tread's and the Tenacity mastery which will give you enough tenacity to walk out of his W's landing area until his stun is ~level 3, and flash/dash/jump out of it at any time except level 5 stun.
Second, call your jungler. Veigar is supremely immobile, and does not have the damage to kill 2 people when ganked or the safety to survive most ganks. His E is powerful, but if he pushes even a bit a jungler can come from the enemy jungle side and gank for a free kill or flash. Even if the wave is pushed to his turret he can max W and farm, which leaves him with free farm.
Third, if all else fails get a Banshee's Veil. Veigar CANNOT kill you at that point until very late game: any spell of his you block will ruin his combo (without E he can't land W, without Q he lost a lot of damage and has low kill potential, and without W/R he lost most of his damage).