Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
Why Veigar, why now?
With the mage update in 6.9, Veigar support became much more viable. Instead of only gaining passive AP form minion kills with Q, he gains it from poking enemy champions as well. This makes it easy for you to stack legitimate amounts of AP from harass.
The Stun Circle was always great, and the main reason why Veigar saw some support play beforehand. This is a great tool in teamfights, and the slow ramp of damage makes you a viable support with the ability to peel somewhat and execute soft targets.
How to play?
Try to poke with Q whenever you can to gain the AP stacks and Frostfang gold, don't get killed though.
When the enemy initiates or gets too close, try to trap them with E, then if they get sunned, W on them. Use the R to execute if they get low. Don't try to steal kills, but don't worry about it if it happens.
In team fights, stay safe in the back line, catch them with E when they try to dive or initiate, or when you can catch them as they run away. A 2.5 second stun is more than enough time for your squad to do serious damage.
Mastery / Runes
Run of the Mill caster support. Stormrider's Surge is great because it gives you the ability to reposition after you Combo somebody, your mission isn't primarily to kill, so that is why i take it instead of
Runic Armor increases the healing gained from Rod of Ages, so that is why i elect for this one.
Standard AP carry runes here.
Quints 3x Movement Speed -This is great for positioning and survivability. Veigar gains AP so easily, that 15 AP seems fairly trivial when this will allow you to be able to maneuver much more easily, and get in range for your stun.
6x Scaling CDR- This gives 10% CDR at 18, with 20% from Morellonomicon and 10% from Eye of the Watchers, this puts you at maximum CDR, to make the most out of your kit.
Scaling health over Scaling Armor. I feel that this build has a decent amount of health in it already, where it lacks armor entirely. This is why I elect for these.
High (decending in threat)
Morgana - Her spell shield allows her target to walk right through your stun, this is bad, but sometimes you can catch her off guard.
Sivir- Her spellshield is also good, but your E has a lower cooldown because she usually maxes spellshield last. Try to bait it out of her, then catch her again when it is down. If you have high skill, you can cast E, wait for her to pop spell shield, then try to hit her with Q before she walks into the circle, but this occurs very quickly and is difficult to pull off.
Thresh/Biltz- Don't get grabbed, you are soft with no escape.
Ezreal - He can teleport out of your ring, so try to catch him when it's down. I don't know if the cooldown is higher than your ring or not.
Tank Supports in general, because you have much lower kill potential against them.
Brand/Zyra - I have not played against many, but I assume are high because they are strong after the rework, and Veigar is susceptible to stun/roots/damage
I have easily forgotten many, be wary.