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.
This build focuses around farming lots of AP to dominate mid-game, thus the rush on RoA and CDR boots - once those two items are complete you can lay back your farming a bit and focus more on ganking. (However Veigar, especially with Teleport, is a *very* gank-happy champion and I tend to gank numerous times before I even manage to finish my RoA)
Ignite is picked instead of Flash because it guarantees you kills in mid-game, which Flash might not - but feel free to change it depending on your playstyle. If you need a more defensive game, roll Flash instead.
Note: If enemies start stacking magic resist, I buy a Haunting Guise somewhere along the line then sell it to finish Void Staff (if the game goes on that long, which it usually doesn't).
I am naming this an "experimental" build since it deviates from the well-proven Sorcerer's Shoes + DFG combination, in hopes for a better early-game farm due to being able to complete Tear + Lucidity boots on the first trip back instead of a Codex and thus being able to stay in lane longer, with more mana regen and faster farming.