Who is Veigar?
Veigar is a High burst AP caster. He excels in farming, assassinating the enemy APs, and following up initiates in team fights. Your Job as veigar is to 1. Farm well 2. Smoosh Squishy APs 3. Peel for your ADC or follow up initiates with his playpen.
When to pick Veigar.
While Veigar is a fun champion, he shouldn't be picked into everything. When I mid I see the role as a 1 1/2 v 1 1/2 lane. Jungler's impact mid on veigar a whole hell of a lot. Veigar is best picked against farm champions with little CC or burst casters who depend on skill shots.
Veigar pairs great with junglers who have a gap closer or hard CC. If your jungle has both, you already know mid is 90% won post 6. The same jungles that pair great with Veigar are also the best against him.
I suggest you do not pick Veigar into a game where the jungle has a hard CC and mid has high burst, as most of the time mids who have CC/burst can be avoided or zoned. With a jungler who can gap close/flash onto you into a hard CC or burst cycle can often lead to a quick death.