Paleobiologists, paleontologists and archaeologists strive for one thing; to preserve their finds in as original a state as possible. You can mount a fossil with an epoxy or cement, which even some museums do. A better choice is to use archival-quality glue mounts and fishing line; you'll see fossils mounted like this in Chicago's Field Museum and the London Museum of Natural History.
Buy a shadow box from a framing or craft supply store. These are typically one to two inches deep, for presentation of three-dimensional keepsakes like medals, flags and grooms' corsages. They are also excellent for fossils. If the fossil does not fit under the glass, you can mount the fossil in your shadow box without the glass. If no shadow box fits your fossil, you can cut a square of pressboard or melamine, and mount it without a frame.
Spray the inside of the shadow box (or your mounting board) with a neutral-colored paint like khaki or clamshell white. These boxes are typically plain white cardboard. You may also line the box or board with vellum, velvet or even a map of where you found the fossil.
Lay your fossil in the shadow box liner or on its board. If the fossil is small or light enough, mount it using Glue Dots. These are a clear, double-sided, non-hardening and archival quality adhesive product which will hold the fossil in place and remain soft so that you can remove it without damage.
Secure the fossil with fishing line or wire if it is too heavy for the glue dots alone. Mark two to four points through which you can thread fishing line to hold up your fossil (more points for a larger fossil). Drill these points, or punch through them with an awl. Thread fishing line through the liner from the back. Tie the fossil securely so that it stays in place when the box stands straight up.
Create a label for your shadow box. This should identify the fossil (perhaps by latin taxonomy---"charcaris megalodon," for example); the date found; and the location (for example, "Lake Turkana, Ethiopia;" "Olduvai Gorge, Tanzania"). Affix this label to the box or the bottom edge of the shadow box. You should now have a museum-quality presentation of your fossil.
Keep your fossil out of direct sunlight. They are calcified and rock like, but direct sunlight can make them brittle.