When casing (casing is wetting the leather in preparation for carving) your leather you would dampen the leather with a sponge first on the back (sueded - rough side) and then on the top (smooth-flesh) side.
You do the top of the leather last because if you wet the smooth side you and then lay it on your marble and the working surface has any dust etc on it, you will immediately have that dirt and dust on your clean leather surface.
After having wet the leather, let it sit until it turns a lighter tan (almost as if the leather is blushing) and feels cool to the touch.
On thinner leathers you can just wet the top because it does not take too much for the leather to absorb the water into the internal layers of the leather.
For backgrounding, the leather should be a little dryer than for normal stamping and tooling leather moisture content.
If you are having difficulty getting your background smooth and even without tool marks when using a leather backgrounder such as the A104. your leather is probably too wet.By Standing Bear's Trading Post from Reseda, CA. http://www.sbearstradingpost.com