Veigar can either be late game or early game depending on the build and who you take on in mid lane. The way I have the runes set up, and skill order he can be strong early but is complete dominance late game.

CDR, magic pen, and ability power are the most important attributes to vieg. His basic attacks are worthless and he is all about burst. as soon as he gets his burst back, he is worth something. Magic pen is what makes all that ap count. AP is self explanatory.

The items listed above are the recommended build for the chance that you are pretty well fed and will continue to stay that way. a single wrong item can turn veigar, into a corpse time after time.

here are some other situational items that work well.

banshee's veil- good mana, and hp. defensive option. the mana will help get some extra ap too
abyssal scepter- some ap, and magic resist but best of all, a decrease in magic resist to all enemy champs near u. great for that guy thats building defensivly bcus u **** him up too much.
void staff- some ap and magic pen.
moonfire spellblade- some ap, tenacity is good for cc toons (sion, fids, morgana, lux, annie)
mejas soulstealer- if your having a good early game with 2 or more kills before lvl 6, this would be an exellent idea.
morellos evil tome- good for some extra cdr, but remember the cap is at 40%

items not to get:
sheen/lich bane/trin force- so what, some ap and mana. ur paying to much for a passive thats worthless to veig.
rod of ages- takes to long to build up, not worth it. save it for ryze.
zhonyas hourglass- nice ap but waste. what are you going to while ur untargetable? waste of money and item slot.

early game you should start with a level of your q then get w then e. max out w so then you can harass well as destroy groups of creeps. the stun is realy good to have just in case of a potential gank. dark matter should be cast on the ranged minions once they settle in one spot and stop moving. Then they should have little amounts of hp. last hit one with your q to gain extra ap, then procede to auto attack.

Always know what enemies stack ap. about mid game is when 2v3s and 3v3s come about. that is the only time vieg should initiate. first pop stun. make sure if you dont use smart cast, that the edges are where they are currently standing. the stun only works if they run into the side of the fence. then upon stun cast dark matter on thier present location. pop ulti on whoever has most ap, throw on ignite, and use q. once all ur abilities are on cd back out for a little bit. basic attacks are worthless, so run out after burst.

Veigar's W ability, is an aoe. you have to watch and look for a pattern in your opponents movement during laning so that you can guess where do drop that bomb.

Veigar also has a very special passive with his q ability. last hits with q earn him 1 extra ap. champ kills also award him with ap. the best part is, theres no cap.

the stun is very unique. its the only ability he has that i dont put on smartcast because it doesnt sun everything in the cast area, only whats on the border of it. plan accordingly.