Who I am:

I'm AiwuZhan, and yes I'm only silver but I believe this off meta build can carry well beyond that. You can check my op.gg here : http://oce.op.gg/summoner/userName=AiWuZhan

I have a 67% win rate with Veigar right now with the build I am going to show you. You are all welcome to add me on League if you want, but I'm only silver...¯\_(ツ)_/¯

Veigar is an incredibly powerful control mage with late game scaling. The only reason I play him top is because of my specific rune build and itemization which many pros use. He can easily hard carry games as long as you play carefully.

Very simply, you should be aiming to freeze the wave in front of your tower. Make sure the wave doesn't crash however, otherwise they can harass you under tower and cause you to lose cs. Use your Q and autos to farm. Do not use your W unless the wave is going to crash into your tower soon. I also do not recommending using Qs for poke, because you run out of mana very quickly even after buying Lost Chapter. After each item purchase, I perform a damage check. This is important in my opinion because your enemy laner will have no idea what your damage capability is. This helps you to gage whether or not you can solo kill your opponent. However you should get Hextech GLP first before even trying to solo kill them, because it is a very strong power spike. Auto the enemy laner every time there is an opportunity, like when they start walking towards you, or walking up to kill a minion. Your autos slow because of Glacial Augment which allows you to get in at least 3-4 before they are able to back away. Early game this is very powerful since most of your damage comes from autos and they cannot respond unless they are a ranged champion.

Assuming you haven't inted and have farmed steadily, you should have 2-3 items completed already, so you should have Sorcerer's Boots, Hextech GLP and maybe Twin Shadows/Zhonya's./Banshee's depending on the game. If the enemy team has a fed ad mid, jg, or adc, I strongly recommend getting Hourglass. If they are not that fed or you are confident, stick with Seeker's, which is a component for Hourglass. Banshee's Veil, obviously is for fed ap enemies. If your team is doing well and the enemy do not have fed champions then go for Twin Shadows, which when combined with Hextech GLP, will turn you into the beast of control. You should farm side lanes when you have teleport available, otherwise it's probably best to stick with your team since your CC and damage can come in handy. Group with your team for objectives because your spells do a lot of damage once you have 2-3 items and the enemy cannot contest. At this point the game is quite literally in your hands. It doesn't matter if your team has been running it down mid and inting because Veigar is truly a one yordle army. When I'm taking Drake/Rift herald, I stand on the edge of the pit opposite the blast cone, right in the center. This way I can place a ward on the other side of the pit. If the enemy come to try and contest, use Hextech GLP as soon as they come into vision from your ward. While they're slowed, use your E over the wall to guarantee a stun or extremely powerful zoning. While they're stunned/trapped in your cage, fire off your spells. This will chunk down even tanks to 2/3 or 1/2 health and might even kill squishies outright. This way you get free objective and you can follow up with Twin Shadows to chase them down or disengage. You want to come into the pit and contest? Nu-uh no way. Want to chase me? No chance. Want to run away? Good luck. Want to funnel into an entrance? Say goodbye to your team.

By now you should have an almost completed build, which means you should be at the back line, helping peel for your ADC and creating pressure by spamming your spells. However, I recommend you keep your E for when your team hard engages or they engage. It is very important as a Veigar to stay alive and avoid being picked off because without you your team will lack very powerful poke, burst and CC. You can group with your team and set up picks very easily with your long ranged Twin Shadows. Once you get a pick, threaten objectives since they can't contest with a team mate down. The longer the game goes for, technically the better for you since Veigar's passive scales infinitely, like Nasus's.

Please vote for my build if you think it's helpful and interesting and feel free to comment on what else I should add, currently I am adding more counters.