Yay, more origami! That's quite some menagerie you've got there, good looking, too! Also, I quite like how all of them (well almost) are the same colour.
I know things can be a bit frustrating at first but it will get better with practice. So don't give up!
As for kami (i.e. origami paper), it's really more fun to fold and it usually gives nicer results. But it's not suitable for wet folding. For that you want a much heavier, sturdier paper like elephant hide or even aquarell or pastel paper.
Basic instructions: Take a large sheet (at least 20 by 20 cm, larger if the model is more complex) because multiple layers will soon get quite thick. Dampen it with a cloth from both sides, but don't overdo it. The paper should feel leathery, not soggy. Then you'll probably have to cut the sheet to a square again since the paper expands unevenly (with and against the grain).
Then fold the model. You might have to redampen the paper from time to time if it begins to feel dry especially at the edges and corners (probably not necessary with simple models). This will allow you to sculpt the model with curves rather than just folds.
When finished, let the paper dry. You might have to fix the shape until then. A hairdryer might accelerate things.