Veigar has many uses in a teamfight. This can be seen in ways like protecting your carries from the enemy using your E-Event horizon to zone off or stun champions from persuing the squishies.
Example: Zed ulting the adc: what do you do? you can place your cage around the adc right behind their back so the moment Zed comes out of R he will be stunned and killed for it.
Another example as why Veigar is good at teamfighting is his ability to zone off people from their teams.
Example: spliting a team down the middle using the cage to pick off one side of the enemy team.

Veigar after 25mins usually has enough (Q)Baleful Strike- (W)Dark Matter burst to steal objectives from most junglers besides Evelynn(her Last Caress Smite burst is up in the 3k damage mark)
Another good thing about veigar's burst if paired with your jungler you can easily sneak/execute Baron/Dragon plays quick enough without alerting the enemy team for being gone for too long.

It isnt a must need but we all know mages love the sweet sweet blue buff. more stacks more mana. If you can try to get it.

The stacking goals on veigar are pretty simple similar to CS.
@10mins/100stacks @20mins/200stacks @30mins/300stacks
this should be your average/bare minimum. usually for me after 20mins ill be at 250, and 30mins ill be at 400+/-. this all will depend how your game goes and you keeping track of all cs being attempted to be stacked.

I said it in the notes for runes for electrocute but the ONLY rune I use.
I do this because I believe Electrocute is ultimately the best rune for Veigar
First reason to go Electrocute is because it has a .25 ap ratio
Second reason: Your EWQ or Everfrost WQ combo will proc Electrocute
Third reason: After procing Electrocute they'll have lower health to allow you to finish off with Primordial Burst to snowball quicker.

doing the numbers on a target with 3000hp and 130 armor and mr. With Veigar at level 16, Everfrost, Deathcap, and Voidstaff. Going electrocute your burst combo will finish with 2756damage burst combo and going First strike which isnt always going to be up for your 9% extra damage leaves you at 2436 damage. an almost 300 damage difference