Pros

-Fast burst damage (If combo is performed correctly)
-Stun is fantastic, helps yourself in attack and defense, and aids in jungler ganks.
-Scales very well into late game with items and Q passive.

Cons
-Very squishy (Before Hourglass)
-Targeted first in most engagements
-Need to learn Veigar combo to be proficient.
-Requires use of Smartcast

Runes.

Mark - Magic penetration, essential in almost all AP mid builds.

Seals - Extra mana regen will help with laning and sustain. Could put AP/level if you really wanted to.

Glyphs - AP per levels help very well with Veigar mid - late game. Could also put flat MR if you were versing champs who harass Veigar well.

Normal AP masteries.

Utility tree - 3 in mana regen helps in lane farming, point in extended buff duration also helps Veigar when getting blue buff from jungle.

Boots and 3 pots ALWAYS. NEVER go Dorans on Veigar, he will lose in sustain so easily and get bullied out of lane.

Rush DFG for huge burst potential at level 6. Rabadon and Void Staff are the usual AP items, helps with the burst and getting through the enemy MR.

Hourglass is essential heading into late game, as it allows Veigar to stay alive after the burst, which should be completed in under 2 seconds.

Last item is mostly enemy dependent. More AP, go with the Archangel. Banshee to last in team fights longer, after popping Hourglass.

Max Q first, for harass in lane. DON'T farm with it though, the extra AP isn't worth having no mana or ability to harass the enemy. Use Q to harass enemy, causes quite the damage early on.

Max E after Q, some may say that you should level W for more damage, but what's the use of that if your stun runs out before you can get the W to land? That's why E should be leveled after Q.

Obviously, W after E, and R whenever you can.

Veigar combo!

Make sure you smart cast Q,W,R and Item 1. Item 1 should be your DFG. Removes the need to click for each spell, you should be able to put your combo down in 1-2 seconds easy!

Skill sequence should be E, W, 1, R, Q. Very good burst and alot of damage!

Be sure to run to the back of your team after your burst, use Hourglass if need be. However make sure to use your E and Q after the initial fight, becomes very useful to catching retreating enemies.

Farm with your auto attacks, not Q!

Harass with Q, look to use your stun, W, Q combo, to get in the heads of the enemy. It will scare them off, trust me!

Get blue as often as you can, when you do, go mad with your skills! Farm with Q, push the lane, just don't get ganked.

Buy 2 wards if possible, handy for laning so you don't get ganked.

Use the bush to your advantage, lead an enemy in, and burst them down!

If you farm well, hold your lane, harass and get that combo down, Veigar should run all over the enemy AP and scare the living daylights of the enemy team. Hope this guide helps you to become the "5 Click Death". Best of luck and see you on the fields!