I am creating this guide as a main (Rank 7 My Champ Mastery). I believe Veigar is an underplayed champion and Will Proceed to tell you why you should not be scared to choose him as a support.

Pros:
+ Infinite AP Rabadon's Deathcap
+ Longer the game, stronger you are (deletes everyone eventually)
+ Full build and too much gold to use? Replace damage for tank, you have infinite AP)

Cons:
- No Built in Movement Increase
- Super Squishy (Unless you build tank)
- No Early Game Damage

I take Exhaust and Flash. If you don't need Exhaust, then take Teleport as it will get you near a fight (or back to lane) quicker.
Flash: Since you don't have a gap closer, this is it.
Teleport: Used to get back to lane after roaming or to get into a fight.

Phenomenal Evil Power:(Passive) The most important part of why Veigar isn't a troll pick any more. This is the main way you are gaining stacks as support. All you are doing as a support is poking down the enemies for your ADC to finish off. Why not get rewarded for doing just that?

Baleful Strike(Q): This is the main source of your stacks with your passive.

Dark Matter(W): The hardest hitting spell in the game. Why not use it?

Event Horizon(E): As a support you need cc. This is a big ring of CC. When you poke down the enemy, hit them with this spell to let your ADC easily finish them off. This spell can also be used to zone out an area for 3 seconds.

Primordial Burst(R): Point and Click. Heavy Hitting. Shall I say more?

I tend to take Baleful Strike first so I can start getting stacks as soon as possible. Then I take Event Horizon second so if any jungler ganks early I can trap an enemy for an assist or be able to get to safety. Then I take Dark Matter so I can spam strategically place more abilities for more stacks.

Always level up Primordial Burstas it is available. As a support, the longer the stun, the longer my ADC has to hit the stunned enemies. This being said, I max Event Horizon first. After that I tend to max Dark Matter next as it has more and more damage. Then last I max Baleful Strike as it is last. You can max Baleful Strike before Dark Matter to get more stacks quicker.

When you have the mana, try lining up both enemies and hitting them both with Baleful Strike to get the quickest mana. If possible, get then close together then stun then and use all your moves on both of them. I tend to stop spamming strategically placing moves when I have just enough mana for Event Horizon. You can roam to mid if your mid lane is pushed against your turret. Just remember that the longer you are out of lane, the less AP you're getting.

Thunderlord's Decree is a must for him, just whenever you burst them and don't have your Primordial Burst ready, make sure to throw in an auto to proc it. Everything in the first skill tree increases your damage dealt. In the second skill tree I like the increased movement speed as it could help get away sometimes. I also like getting mana from health pots as the removed mana pots. Regenning mana = more spells to use. Increased CDR because why not.

MRes to help protect against emeny mages from deleting you early.
DR to gain stacks just that much quicker (You can take Armor to protect from ADC).
MPen so you can damage tanks more.
AP for more damage early game.

See Item Notes Above.