Say for example you knocked an opponent to the ground. What would you generally follow with afterwards (if you're close to them)? I'm not saying like "OMG I ONLY DO THIS" as I'm sure that there's more to wakeup games.
Here's a few options.
1. Overhead
Since the opponent is prone to blocking low when they wake up, you can do an overhead attack to hit them. And maybe in the case of 2k2 (and you're l33t), overhead BC cancel into meaty combo. Also if I'm correct, in the case of Ryo if the timing is a little off, they can roll forward to escape your f+A overhead chop, and hit you from behind.
2. Low attack/sweep
This is assuming that your opponent is thinking (double assumption

3. Grab
If your character has a grab move you just grab them when they get up. I personally don't use this often (I don't use grapplers), but actually against a Clark player I usually get grabbed, because if you jump he's probably doing a close C, and if you don't he'll SAB you. And this can repeat until you get broken out of their effective range.
4. Throws
Similar to above, just that I'm not grasping the timing very well - a viable option, but it can be breakable.
5. Jump attack/Hop attack
Probably the worst IMHO, you're very likely to get

6. Do nothing/Block
It's great against opponents who are

