The current conservation standard is that all archival mounting should be reversible, so you have options. I usually hinge mount with linen tape. The tape has a starch adhesive that you wet and press into place. There is self-adhesive linen tape, but this is not widely accepted as archival.
The way this works is you take one piece of tape, maybe an inch long or so and fix it to the edge of the back of the print so the sticky side is facing the same way as the print surface and you've got a tab of tape sticking out about the width of the tape. For a small print, you should only need about 1/4" of tape contacting the back of the print. Then you position the print on the backing board and use another piece of tape maybe two inches long to tape across the tab that's sticking out, forming a "T" shape, to the back of the board. One or two of these "T" hinges is usually sufficient, but you may need more for a large print. Then you mat over the edges of the print, so the hinges won't be seen in the frame.
To remove the tape just dampen the back of the tape, allow the adhesive to soften for a minute or two, and remove it.
Flush mounting on the same size board as the print in a reversible way is trickier. You could use mounting corners, if you don't think that would detract from the presentation.