It's best, if you have the time, to let the paper dry for two or three hours, or overnight, even if you plan to work with it wet. Staples tear holes in the paper if it shrinks too much, leave rust stains, and cause further damage when you try to pry them out with a screwdriver. Then I hit on a method that is extremely strong yet leaves minimal traces on the paper. For best results the mounting board should be a good quality plywood, not particle board. The sticks distribute pressure over a larger area of the sheet and grip the paper with the texture of their grain, which eliminates tearing.
Wood quickly wicks up moisture around the staples, eliminating rust stains.
When time comes to pry the staples out with a screwdriver, the wood takes all the abuse caused by forcing the screwdriver under the staple. And the method requires many fewer staples, making it faster to do. The only catch is that each stick covers a small area of the sheet. As these areas are narrow and close to the edge, I just paint to the edges of the sheet firmly stapled, then pop the sticks off one at a time to finish painting to the deckle. If necessary, the sticks can be remounted after the paint has dried.