The goods ;D!

Pretty much kill every champion in the game with one combo.
AoE Stun
Strong Mid and Beast Late

The Bads

A useless midget early game
No mobility
Easily focused in team fights
Not a great AoE team fighter

Baleful Strike : This skill has alright base damage, an average ratio and a good mana cost. Farm Baleful Strike all day because you gain a stack of AP with every minion killed with it. Prioritize siege minions because they give double the AP.

Dark Matter : Very high damage AoE nuke (High base + ratio). Why not max it first? Because, Veigar is more of a passive laner and you should prioritize farming on your Baleful Strike.

Event Horizon : His E is an AoE stun with a high cool down. The skill Event Horizon Forms a circle that stuns anyone who attempts to pass through it.

Primordial Burst : In my opinion, this is the strongest single target burst skill in this game. It has a very high ratio and base damage and also does more damage based on the amount of ability power your opponent has.

Tear of the Goddess : This item is a fantastic item to rush because it increases your sustain. This will allow you to stay in lane and farm to your heart's desire and also you can trade and still have mana afterwards. (If you ever rush Seraph's Embrace without getting another item than you should delete your account)

Negatron Cloak : Going against LeBlanc and cannot farm whatsoever? Build this item because farming is your main priority, this item will keep you alive so you have somewhat of a chance.

Seeker's Armguard : Build this if your opponent is someone like zed or talon who can immediately kill you are level 6 if you do not have adequate armor.

Fiendish Codex : This item is built if you are snowballing very quickly (20 CS ahead and you have 2 kills?) rushing a Deathfire Grasp Is a wise choice because it is very easy to snowball with it.

Veigar is a passive laner that never stops scaling.

His early game is a joke and a majority of time the enemy will try to force you out of lane.

Trying to win trades in lane is sometimes difficult without depriving yourself of mana.

Assistance from a jungler greatly influences this lane because veigar snowballs easily.

You can start to be aggressive at about level 5 and than at level 6 you can attempt to nuke your opponent.