I won't write much here, cuz if you're like me you don't read this anyway. Most of what you need to do is up there.

Using his abilities are simple:

1. Event Horizon: stuns them so you can use
2. Dark Matter: takes a second or two to hit, so in the mean time use
3. Baleful Strike: deals a fair amount of damage
4. Primordial Burst: finishes them off, especially if they use a lot of AP.

Note: Make sure to use Baleful Strike early and often to finish off minions. Its best feature is that it gives you 1 AP for every kill you get with it and minions count. Don't be afraid to use Clarity early to help you do this.

There is a simple rule of thumb with Veigar: When in doubt, put the point in Event Horizon. Even if the player is smart and avoids the edges, they're confined to that little area and you or your team can do massive damage to him.

Notice the Morello's Evil Tome and Frozen Heart. These items really up Veigar. He does burst damage, but when that burst is done, he's kinda useless late game. They reduce your ability cool downs by 40% total. This means you can hit an enemy with everything and by the time you've used it all, Baleful Strike will probably be ready if you need to finish the job.

If you can't buy an item outright, get the ones leading up to it, they are all great to have.