I think the biggest thing with a character like Superman is that you have to feel when a special attack is coming. Every Superman player, if he/she relies on specials too much, will show a pattern from the very start of the match. Then it's just a matter of knowing what to do when that special comes your way.
For the ground pound, you have no option but to jump. If you're a character who can do a special from the air, like Sonya or Kano, this is the time to unleash it. As Superman does the ground pound, jump toward him and whoop him with the Downward Bicycle Kick, Cannon Ball, or whatever you got, even just a kick if you're any ol' character.
His laser, I find the most annoying, just because you can't jump over it like most projectiles (Superman can kiss the fattest ass in the world). You're gonna have to duck or do a low move if you're close enough to get him. I use Sonya and her projectile is downward, so that gets him. I dunno how many characters have this.
Your opponent is probably gonna love flying up to do a ground pound or laser. It's very important to anticipate this move. Again, if you're Sonya, Kitana, or Kano, Square-Wave-Punch or CannonBall him when he does this. Joker's Magic Trick, 3 also does the trick. (I dunno who you play as, so it's hard to give specific tips).
If you read your opponent's pattern and anticipate Superman's specials, you will have what you need to overpower him. Players who rely heavily on specials and specials alone tend to be unskilled when it comes to close-quarters. That'll be your chance to pummel Superman with the best combo/juggle you've got. Just make sure to unleash it as soon as you're close to him before he can do his annoying litlte kicks on you.
I might be able to help you out more if you tell me which characters you usually play as. Maybe I've tried them out, too, and can give you more specific tips.
EDIT: As soon as the match start, try to go straight into ass-kicking, offensive move. If you're able to stick close to him before he gets away to do his little specials, you'll have a better chance of dealing as much damage as possible before he has a chance to start his chain o' specials. Pick your character's fastest move, even if it's a simple kick or punch, and try to string together as big a sequence of attacks as possible from the get-go.
