Use hanging putty to mount the poster. This tacky, dough-like substance is available at most craft and home supply stores. Apply a pea-sized piece of the dough to each corner and to the center of the poster then stick it to the wall. To remove the poster without harming it, lift up the corners and peel off the putty.
Laminate the poster at a copy supply store. Lamination is typically only a few dollars and allows you to bend and move the poster without harming it. Once it's laminated, you can tack the poster to the wall at the clear plastic corners while preserving the poster itself.
Mount the poster in a poster frame. These frames, available at craft stores, are flat, inexpensive and feature narrow edges. Poster frames typically have a hanger on the back. Once mounted, hang the poster by hammering a nail into the wall then suspending it on the hanger.