First, find a place to set your press. Bolting your press to a workbench works great, but if you can’t, screw your press down to a scrap board or piece of plywood that extends out around the base of the press. Then you can use small c-clamps or screw clamps to attach it to a table, counter top, etc. Be sure to extend the edge of the press off of the mounting surface enough to allow your working clamps to clear.
Second, tape your foam into the press. No need for double sided tape or covering the entire surface with adhesive. Get some simple 2” blue painters tape and make one tape roll across the bottom of the press and two across the top. Stick your foam in place and close the press and apply light clamp pressure for a few minutes. You’re good to go.