You can move underwater at a quarter of your speed as a move action without needing a check. You can move underwater at half your speed as a standard action without needing a check. You can move at your speed as a full round action without needing a check. You can move at half your speed as a move action if you make your check (the water will be considered calm) or at your speed as a standard action if you make your check. If you make a check and fail, you can move at the speeds listed above for if you didn’t make a check.
The exception to the above is if you’re being directly threatened in combat (i.e. in melee). In that case, you have to make a check to move at all, but could then do so at the listed speeds above (if you make your check).
No 5-ft stepping as that doesn’t really make sense unless you somehow can give yourself a swim speed.