Choose a backing for your collage that is made out of a sturdy material such as cardboard. This will help prevent the piece from warping.
Apply glue evenly across the back of the papers you are using for the collage. The glue should cover the entire cardboard backing, all the way to the edges, to prevent warping. Use a popsicle stick to spread the glue.
Varnish the collage with a varnish made for paper, such as Liquitex or Mod Podge. Use a paintbrush to cover the front of the collage with the varnish. Allow to dry completely. Cover the finished collage with a heavy and flat object, such as a book, and leave it alone for at least 24 hours to make sure it doesn't warp.