This is one of those questions that if you line up 12 people, you'll get 12 different answers.
I do mostly smaller sized projects, belts, holsters, knife sheaths, etc.....When I'm about ready to start stamping, I hold the leather under running water till both sides are wet....not soaked, just wet.....let access water run off then set it on the table to dry out just a little....there's a fine line about how dry it should be before starting to stamp....but it is almost back to dry looking b4 I start...then I continue to keep the leather damp with a wet towel as I work......
You'll hear/read about "casing" leather, meaning to soak it then store it in a plastic bag for a certain amount of time b4 working with it....never done that so can't speak to it much. I just do what works for me and my situation.
One thing for sure....you can't stamp when the leather is soaking/spongy wet, nor when it's too dry......got to "hit it" when it's at the stage of drying out that suites you and when you get the result you like....that comes with time in.