Veigar is a very powerful champion. The passive from Q can lead to very quick AP boost. The best ratio is for every 5 minions killed, 3-4 should be killed with Q. That means 100creeps should give 70-80ap boost. Killing enemies will lead you to even more ability power. All you have to do is farm and kill by nuking enemies ;)

Why these runes? Because It's good to have some AP boost, mana regeneration for the beginning of the game especially and good magic penetration. Instead of mana regeneration runes you can take those for cooldown reduction. That helps sometimes if you want to quick farm. Low mana regeneration might be a problem at the beginning, so Clarity spell might get in hand. In the late game with almost 10mp/s regeneration you can stay in battle as long as you want ;)

Masteries like these can help you get some damage boost and stay on ground a little longer. Heavy offensive masteries will give you extra ap boost, 10% magic penetration and extra 5% of ability power. Little magic resist and armor from defensive masteries and little mana regen from ulitity.

Q is VERY important spell. But once you are level 4 your jungler will start ganking your lane. Short, but still, stun will make enemy flash. Once it's done he won't be pushing his lane that much. Also the combination of E W Q R -> flash -> Q is sometimes the best option to nuke on early levels if enemy is harrased from time to time and left with 3/4 of hp.

With this build I usually get around 1.000 AP by the end of the game. It is pretty awesome how fully stacked Archangel can boost a little bit of your ap ;) Anyway this is all you should know about Veigar the Nuke's build. I once did 2.3k ap with 5 archangels and rabaddon's deathcap on a game that last 1.5h and did pentakill with a single meteor ;P That was pretty awesome ;D Hope you enjoy that.