The items in this build are just a framework, it's more of a playstyle than an actual build. The build itself is purely a late-game build, which means early on you won't do much damage and any time spent fighting champions instead of farming will hurt your end-game, as well as the build overall. "So why does this build work?" You may ask. This build works because of Baleful Strike. If you get enough farming done with that skill alone, it won't matter how little you helped your team in the early-mid game. So hang back on your lane and farm whenever possible, avoid using autoattacks so that you can get more Qs in and just get as many stacks on that as you possibly can.

For the items, the priorities are to build as much mana regeneration and cooldown reduction as you possibly can, maxing your Baleful Strike first so that you can farm as much ability power on it as humanly possible. I take flash/barrier summoner spells to help my mobility and survivability throughout the game, particularly early on when I don't have much damage to scare the enemies off with. The damage of Baleful Strike allows Veigar to effectively farm under tower, so feel free to hide there and play it safe. Do not waste your mana harassing your laning opponent. You don't have enough damage to chase them off lane and you don't have enough mana to harass and farm at the same time, so just conserve it.

As for an actual build order, you should start with mana regeneration, first going to lane with two faerie charms and 3 health pots, building a tear and two more charms when you return. Next you want your Chalice of Harmony, soon to be build into an Unholy grail. Following that you'll want to finish your boots, there are three primary options for boots; Mercury Treads, Boots of Swiftness of Sorceror's Shoes. I would suggest Mercury treads a majority of the time, since combining it with barrier will get you out of a lot of hairy situations, however swiftness boots can help you outmaneuver and kill enemies. I wouldn't suggest you build Sorceror's shoes unless the enemies are completely ignoring you, though even then I would recommend Swiftness first. Enchant your choice of boots with either Alacrity or Distortion, and start working on Morellonomicon. Following that, make an Archangel's out of the Tear we started with. This is about the point in the match where you'll start really hurting.

When you finish Archangels', you should have around 500-600 ap, assuming you've farmed reasonably well. Here you're faced with a choice between Rabadon's Deathcap, Deathfire Grasp, Zhonya's Hourglass or Void Staff. To make this decision, consider your situation and adapt accordingly. Rabadon's is important and should be kept, but I often put it off untill last so that I can get Void Staff for penetration or Zhonya's for survivability. If you're struggling against tanks, or getting focused, I'd suggest you do the same. I only get Deathfire Grasp when I'm confident in either my ability to avoid harm or my team's ability to cover for me.

All said and done, 30 minutes into a match anyone using this build should have upwards of 150 ap coming from their Q and be just finishing their 5th item, which should put them at approximately 700 ability power, unless they took Rabadon's for their 5th, which would put them around 850-900. This is when the build shines. At this point in the match, Veigar will be doing so much damage he can tear down any enemy, meaning that as long as he can stay out of the line of fire he can melt the enemy team almost single-handedly.

Personal record with this build; 1300 ability power, 50 minutes.

I dare you to top it.