For the not too archivally squeamish, you can brush on a moderately thick coating of Miracle Muck or LaminAll on the back of the print. Don't go all the way to edges, that's why you had all that stay-inside-the-lines training with coloring books. Let it dry. Then drymount it to a backing, those particular glues act like drymounting tissue at temps above about 170F or so.
Or you can tack on about 2 layers of a special drymount film called Fusion 4000 directly to the back of the print. Fusion 4000 is a thin film of just the glue component of drymount tissue, minus the paper support. You can fold it, lay it down in sloppy layers that are thicker in one place than another, etc, and will it work itself out nicely under the heat with no bumps. BTW two layers works great for canvas.
Or lay a piece of regular drymount tissue over the back of the print. With a magic marker trace out a shape that is a little smaller than the artwork. Cut the drymount just inside the marker lines, if you have a swivel knife so much the better. Then tack it to the back of the print and proceed to the press.
edit, or you can apply the glue and while it is wet very carefully push it down onto a substrate. No press required. If you didn't apply so much glue that it will ooze out you can cover the artwork with a cover sheet (silicone release paper is nice) and burnish it down with a roller or just your hand. This is how we mount my wife's pastel drawings. If you have a vacuum press use it but don't fret if you don't, they're way over rated.