Examine the construction of the back of your shadowbox. There may be a wire for hanging, or the shadowbox may have hardware to help you hang it.
Determine the best location for your shadowbox, preferably out of direct sunlight. Though a shadowbox will help prevent fading, direct light will undermine its usefulness. Where you hang it will depend on the layout of your home. Consider the locations of furniture and other artwork on your walls before placing the shadowbox.
Using a level, hold your shadowbox up to the wall. Mark a light line in pencil along the top of the shadowbox, stopping a few inches short of each edge of the frame. Make marks at the side edges of the shadowbox as well if you think you'll need help aligning it on the wall.
Hammer a nail into the wall at each end of the line you marked across the top of the frame, unless your shadowbox has hanging hardware on the back. If it does, place the nails appropriately for the hardware.
Hang your shadowbox from the nails on the wall carefully, straightening it out as necessary by lining it up with the marks made earlier. Line your shadowbox up with the appropriate hardware, or let the bottom of the top piece of the frame rest atop the nails.