First off, I use hide glue as it was most certainly what was originally used on an antique and it will reactivate itself. You may be able to use the "liquid" version that does not require keeping the glue hot. Using this glue, then, rules out some unconventional options (contact cement, iron-on, etc.)

Two complicating factors are
- if there is any curvature to the piece
- if there is existing finish on the show side.

If it's flat:
- lightly clean the crystallized glue off the substrate and back of the veneer.
- apply a light coat of hide glue over the back of the veneer and position the piece in place
- apply a caul of some type of sheet goods (MDF, plywood, etc.) and clamp it down in as many places as possible
- let the glue dry overnight at least. Clean up squeeze out with warm water on a rag.

If it's curved, you have more problems. This is often done by a process called "hammer veneering" where a veneer hammer is used like a squeegee to press the veneer down onto the hot glue while it gels and cools. But this really needs unfinished veneer. Another option would be to proceed as above, but use a vacuum veneer press to hold and clamp the veneer in place. This could be really tricky and may require you to disassemble the drawer front.