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.
Veigar. He is tiny, and he is evil, and he can pack one heck of a punch.
Under most circumstances it works best to have Veigar solo mid. At least with the way I play him with this build. Starting with a sapphire crystal and one of each potion you simply need a lot of patience in mid to AP farm EVERY MINION YOU CAN WITH BALEFUL STRIKE for the first 8 or so minutes. You should first recall when you have 1275 gold and purchase a catalyst and boots of speed. Teleporting back allows you to not miss any time with the laning phase. It is very possible to rack up 80 or so AP before buying any AP items once you get the hang of last hitting with Baleful Strike.
Every now and then, fire a baleful strike the enemy hero you are facing to see if its dealing a good deal of damage to them. If it is, you can try to combo off a e,w,q,r. Even early game that can deal beastly amounts of damage. As your build develops, deathfire grasps will become one of your best friends as your combo changes into e,w,3,q,r (3 is the hotkey that I store deathfire grasp). Even high HP champions fall to this very quickly unless they are stacking magic resist.
Late game, your job is to erase one member of their team before any team fight even starts. Usually aiming for the highest AP member on their team, or a low HP DPS. It is not unusual to end with 600-700 AP. My highest AP in a game peaked over 1000.