Ill keep it simple and summarize this quickly.

Domination

Dark Harvest: Dark harvest doesn't have as much early game strength as Electrocute (which procs on Veigar's combo), But considering how much damage veigar does at lv 3, you'll out damage Electrocute in a matter of minutes.

Cheapshot: More damage against stunned or impaired enemies, what else is there to say?

Eyeball Collection: You'll get the stacks for this a lot quicker than the other 2.

Ultimate Hunter: Your ult is very important to finish off anyone under 50-30% health, so you'll want it up a lot.

Sorcery

Absolute Focus: You'll be engaging in most encounters and are likely to have over 70% health, especially since most people avoid Veigar until he's used his cage. So its extra damage.

Gathering Storm: Who doesn't like extra AP?

Scorch:a good substitute for Gathering storm early game, but falls off mid-late game.

P.S. choose adaptive force for the first 2 circles and either Magic Resistance or Armor for the 3rd, depending on the enemy team.

Not much to say here. Relic Shield is a great support item for Veigar, since it allows you to get stacks, while also not stealing gold from your ADC. Sorcerer's Shoes are the best boots for you since they give you magic penetration.

Everfrost is like Luden's Tempest but better. sure it gives you 10 less AP, but with Veigar's passive, that's no problem. The Glp active slows enemies which will let you engage easier. it also helps proc Cheap Shot.

You're gonna wanna go with either Void Staff or Liandry's Torment as your second item, depending on whether the enemy starts building magic resistance or tank items/have a healer.

Rabadon's Deathcap is a good third item. By this point in the game, you should have around 350-450 AP, meaning that rabadon's will bring you near or over 800 AP.

Then you'll want to build the other items in the final build. As for the situational items, Zhonya's Hourglass is a good item to get you out of a sticky situation, and the duration should give you enough time for your cooldowns to go down enough to do your combo again. Twin Shadows is a good item to help you escape or close the distance between you and a enemy. Dark Seal Is a good temporary item if you're confident in your ability to stay alive, but is not worth keeping late game unless you upgrade it to Mejai's Soulstealer

Its pretty simple really.
is a amazing passive. It gives you a single stack per attack landed on a champion, or minion/monster killed with your .
You should focus on killing minions with , but only when your Relic Shield's passive is up. Other than this, use it to poke down enemies until lv 3.
Once you hit lv 3, you're gonna want to use your EWQ combo. E being , W being since it takes 1.2 seconds to land (a tiny bit over stun time on lv 3), and Q being . This combo is enough to chunk someone's health and even kill late game. but your true power comes at LV 6 when you can add R to it for a EWQ R.
Early game, should be used on enemies at 30% or lower health. Mid game this goes up to 50%(for squishies)-30%. And if they're really squishy, you're fed, and are well above 1000 Ap, you can probably 1 shot with your R. Although late game, does enough damage to practically be a ult.

P.S. since takes so much time to land, try to predict enemy movements or attack when they're stunned. its also good to use it behind you while they're chasing if possible. And when a enemy is inside of your and not stunned, aim towards the middle, leaning a little more towards where they're moving.

Most Important Note!!!: only take the kills with your ult if your ADC is not able to. Your Job as a support is to feed your ADC, Not yourself. And don't steal their CS.

Flash & Ghost to get away from enemies or chase them down to get a cage around them.

Flash & Heal if you feel like your adc wont be that good and you might need a way or keeping them alive.

Exhaust and Ignite are good, but Veigar is squishy so you probably don't wanna get that close to them. plus if they're low enough to ignite or exhaust, they're low enough to kill with your ult.

Go out there and have fun being evil.