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.
I suggest Flash and Teleport. Flash is flash and Teleport let's you go bot or top to nab a kill or just let you get to lane faster.
I only use quickcast on w and ult. This allows precise manipulation of q and precise placement of box which I really like. Use what makes you most comfortable.
The purpose of this build is to remove the unfortunate necessity of building inefficient items like morellonomicon.
First lets go over why people go morello's and why its garbage on Veigar.
People go it because Veigar likes mana and he NEEDS CDR.
Seems logical but if we look further into the item we can realize the item is actually terrible for Veigar.
The grievous wounds passive is useless. It only applies when enemies are below 40% HP. If they're below 40% against Veigar... they about to die.
The CDR can be replaced by runes.
The mana can be replaced by meditation.
It gives you 0 survivability. This build focuses on make a kind of tanky Veigar with purchase of early health combined with scaling hp runes. The logic behind this is to avoid making you seem like a weak target that can be quickly killed in fights. If you're not dead you can cast more spells. Each Veigar combo makes someone else not there. The more combos the better.
In conclusion if we itemize, and choose appropriate runes and masteries. We don't have to sink so much into an unnecessary item.
With the change to the way Veigar gets stacks. Going for an early pseudo invade can net a few early stacks. Don't go alone! Make your team tank.
Learning how to lane on Veigar is super critical. Our goal in laning is acquire stacks and acquire dividends. Veigar is a crazy weak laner with his minimal early harass and minimal wave clear. You are pretty much disadvantaged in most matchups. Don't worry about having less last hits than your opponent its almost guaranteed. But your last hits are worth much more than theirs. Your precious AP stacks will carry you through the lane.
General strat: With the passive change harassing enemies is now extreme value. Hitting the enemy mid laner with a spell is about 20 gold worth of ap.
Passive lanes: If they only want to farm, so do you Veigar outscales almost everyone with even late game farm.
Bad lanes: Don't be afraid to play super passive and just last hit from max range with your q. A bunch of these matchups are out there. Remember most champs are stronger than you at this point. You win by not feeding and getting as much money as you can. its alright to miss a few last hits.
Don't be afraid to use flash and Teleport to avoid a gank or get a kill that's what they exist for.
Fight around Box
I can't stress this enough stick to the edge of fights and always fight with box. The spell is insane. If you're playing with friends make sure they understand to fight around it. If you whiff one just make sure you all back off then try again. No need to rush in and die just wait 5 seconds for a new box.
Use box if it catches someone kill them, repeat this process until no enemies remain. You do the most tower damage with lich bane. If you can get a safe lichbane proc on that tower do it.