Sebastian Carter of Rampant Lions Press, Cambridge, UK, has generously written of his paper-damping method as follows -
My method, as described in The Book Becomes [Rampant Lions 1984 - there are several copies available on Abebooks.com at very reasonable prices], was to damp in batches of 25 to 30 sheets, depending on the thickness of the paper, between blankets soaked in a bucket of water. The paper should end up damp but not soggy, otherwise it will repel the ink. I piled the paper and blanket sandwiches wrapped in polythene sheeting for a day, and then took the blankets out and restacked the paper, halving alternate batches so that the damper outer sheets in one batch were against the drier inner ones above and below. I left this pile for another day, and then printed. The dampness evens out very effectively. This method would suit you if you need quite a large run of quite small sheets.
We adapted this method from Peters and Foster at the Vine Press. They used to interleave dry sheets at the middle stage, but we found this increased the risk of the paper wrinkling, so we stopped. Some people advocate weighting the pile, but paper expands significantly when damp, and needs freedom to move, otherwise you do get wrinkling problems.
There is no comparison with dry paper from the point of view of quality of impression. Once you've printed a page of type on a sheet of damped rag paper, you are spoiled for life. But you have to plan ahead, and there's a set-off problem, so you have to have a sheet of paper behind [i.e. between the sheet to be printed and the tympan] if you are backing up. My note in The Book Becomes about the merits of Hostmann Steinberg ink in not setting off was over-optimistic: I think they may have changed the formula, and made it a runnier consistency.
With wood engravings, I found I often ended up not damping. Large areas of black (or colour) tend to stick to the damp paper and be difficult to separate on a powered platen press (no problem peeling off on a hand press). Also, damp paper tends to pick up shallow clearing on a block (very common unless they have been mechanically routed) so you get printed backgrounds where you don't want them. I found I ended up damping in some cases and not in others, even within one book. The Primrose Academy books I printed demonstrate this. The smooth Zerkall was sometimes damped and sometimes not. The special calendered version made for the Society of Wood Engravers did not require damping, ever.