Although there are several glues commonly used in woodworking, contact cement is often the glue of choice for applying veneer. Contact cement does have some drawbacks in that it never hardens completely, but this makes it more easy to remove in comparison to other glues, as well.
Spray the surface lightly with water.
Warm the veneer gently using an iron or a heat gun. Begin the process at one end of the veneer, at a break or at a damaged area; you need to be able to get a putty knife under the veneer. The iron or heat gun needs to be hot enough to soften the cement. Apply the heat for several minutes.
Slide a putty knife under the veneer and pry it up. It should come up fairly easily, but may break into small pieces if it is brittle.
Scrape off any remaining contact cement with the putty knife. If it was solvent-based rather than water-based, use some mineral spirits to soften the cement and better clean the surface under the veneer.