Contact cement is the best glue to use. Make sure the two surfaces don't touch until the veneer is in the proper position, because it can't be repositioned.
Gorilla Glue is the best glue for wood. Put the glue on and hold it in place with a vice. It works great. The frame of my front door was broken and I put the glue on and held it in place. After it dried, I sanded and repainted and you couldn't even tell it was ever broken.