Hello, I am BebsiMax, don't let my rank fool you because i never play ranked and if I play it's either my ping or a failed teamwork.

You are welcome to add on league and have fun with me, my games can be fun :D.

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.
Your main objective is to last hit minions with your Q so that you can stack ability power, you have to be careful at the first 10 minutes because you are squishy at top lane but trust me Veigar has the late game scaling and he will ult other squishies at full health

Now that you have at least Luden's echo and Sorcerer's boots you can get kills like a piece of cake, finishing kills with Q is also important, more stacks more ability power, your W does great damage but is predictable so make sure to land a good E and do your thing, with your current build and ap you should combo squishies like Akali and Ashe to death very easily,
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 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.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 complete 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 Crowd Control. You can group with your team and set up picks very easily with your ranged abilites. 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.

Thank you for reading my guide, I used information based on my experience and other Veigar builds
Please vote for my build if you think it's helpful and interesting and feel free to comment on what else I should add