As veigar pretty much your only goal pre 6 is to farm and get as much feed as you can. Then once you reach level 6 you dominate with your advanced AP and MR pen. This pretty much makes you a unstoppable midlaner unless you are ganked. Veigar has high mana costs but this is fine with Seraphs embrace and his passive. Also his AP ratios are very high since he is relatively close range and slightly skill shot reliant with his W.

Veigars ratios are pretty insane on his abilities including his ult (1.2 ratio on AP) so pure AP and MR pen = TONS OF DAMAGE. To go along with that he has very good mana regen so you can use your Q a ton especially once you get Archangels staff. This full build basically has as much AP and magic penetration as possible to simply MELT tanks and squishys alike.

These synergise with your runes and items pretty well to deal as much damage as possible.

Im kinda lazy so just look at masteries this is basically the same thing.

Pure damage and high amounts of mana make you a high sustained champion lane and bursty champion in teamfights. Also if you get fed enough this can give you 40% cooldown reduction to go along with that. These items basically give you 1k AP with your Q so you shouldnt have too many problems blowing peoples faces off.

Usually in lane you just want to occasionally throw out your Q for some farm and AP and if you basically spray and pray with your W you will eventually hit something. In a harder engage though you usually want to throw your E to the side of somebody to stun them then place down your W and Ult and Q. This just melts high AP casters so much that I have actually 1 shot people with my ult. Thats how much damage you can do. Combining this with the High magic Penetration of your masteries and Runes you can blow up tanks pretty efficently.

Basically when you farm you want to use your Q to finish people off. Usually the easiest way to do this is to left click the weakest minion wait till its health is about 10 below what your Q does and then hit Q to nuke it. This is a pretty effective way to get AP and kep your farm up.

Pros:
-Good at wrecking pretty much anybody later on
-Insane burst
-basically unlimited damage
-Decent CC to go with burst
Cons:
-Ganks= VERY BAD
-cant take multiple people at once usually
-very squishy