Vega was known as the easiest character to dominate with back in the days of Street Fighter II Super Turbo.
Unfortunately for his fans, Capcom has slowly been toning down his effectiveness ever since, with Street Fighter IV being one of his weakest showings yet.
To win with Vega, you need to rely on lots of gimmicks and parlour tricks, as well as staying unpredictable. He has no strong anti-air and no huge combos, so you need to take the lead and then use your mobility to make your opponent chase your around the screen.
Rolling Crystal Flash (back, towards + P)
Vega will roll towards his opponent before stabbing with his claw. It can be cancelled with a Focus Attack at any time while the LP version can be used as a quick poke from distance. The EX version starts faster and does more hits.
Scarlet Terror (down/back, towards + K)
Vega's biggest nerf is undoubtedly here. His Scarlet Terror no longer has the invincibility needed to work as a good reversal, wake-up move, anti-air and so on. It CAN still work as an anti-air but its uses are very specific, while it no longer combos into itself either.
Sky High Claw (down, up + P)
The regular version isn't great but the EX version is brilliant for getting out of corners, as it will cut through the opponent and go right past him. Always worth having meter for this move, in case of emergencies (ie: you've just been thrown into the corner and the opponent is closing in).
Flying Barcelona Attack (down, up + K then P or P+K)
His trademark attack. You can fly past the opponent and hit them from the other side and then once you have them panicking about which way to block, throw them from the air instead. The EX version also hits on the way up. This lets you alternate between jump back HP (has to be blocked high), cr.LK xx EX Flying Barcelona Attack (has to be blocked low) and throw (has to be avoided or teched) on the opponent's wake-up.
Flying Barcelona Special (down/back, down/towards, down/back, up/towards + K)
Vega's more useful Super, as it serves the same purpose as Flying Barcelona Attack but with a
Bloody High Claw (down/back, down/towards, down/back, up/towards + KKK)
Unless you crumple the opponent with a Focus Attack, this is notoriously hard to land. Your best bet is to either go for the aforementioned crumple or try to do the Ultra through your opponent's fireball. Either way, DON'T just guess, as the recovery will almost certainly get you killed.
Basic Combo: cr.LK xx EX Flying Barcelona Attack
Advanced Combo: Jump in HP > cr.MK > cr.MP