From the Homemade Paper site
Take a rolling pin and press down on the pile to squeeze out the extra water. This will also bind the pulp fibers together. Start at one end and roll firmly and evenly across the pile. Do this several times to get as much water out as possible and to press the fibers together.
The hand press option: a small hand press is great for squeezing out the paper. Turn the paper out on a large sheet of wool felt and cover with another sheet of felt as described before. Now squeeze the felt sandwich with the press. Or using the old-fashioned washing machine, feed the felt sandwich through the rollers. Hang it out to dry Now carefully remove the top layer of felt (and any other absorbent materials) from the pulp. It should now hold together as an honest-to-goodness sheet of paper. Carefully take up two corners of the paper by rolling them back (just a half inch/one cm or so) with your fingers. Hold a corner with each hand and gently peel the sheet off the bottom felt.
Clip the fresh sheet on to a laundry line with ordinary clothespins to dry. Any place that's warm and dry will be fine--wherever you would hang laundry. Avoid damp areas (mold might grow on the paper), dusty areas (wet paper will collect any dust in the air), or windy places (your paper could be blown off the line!)
Drying time is about three hours, more if the air is humid or if there is little sun.