I'm going to cover, essentially, the variations on a single method of wall mounting here. My approach is wildly cheap, and can create a number of pretty appealing looks.
Tools and Materials
I do pretty much everything with an Exacto knife, a large cutting mat, and a good quality 24 inch steel ruler. Any standard cutting mat is marked with a good grid, allowing easy cutting of right angles and fairly exact dimensions. For more precise cutting, I measure with the ruler and use light pencil marks. It may be necessary to first correct any un-squareness by recutting materials to exact right angles using the grid on the cutting mat.
With a little practice, cutting papers, mats, and other materials by running the Exacto knife along the edge of the ruler becomes easy. Hold the ruler down firmly. More firmly than you think you need to.
My go-to glue is pH neutral PVA glue. It's essentially just Elmer's white glue, but you know what you're getting. Cheap white glue could, in theory, be something quite different, and might not bond with things you want to adhere. I've never actually seen this occur, but I always buy actual PVA glue because I know it works. It bonds, somewhat to my surprise, to the back side of standard drugstore machine prints perfectly well. For gluing wood, I will often use a designated wood glue, but I see no reason PVA would not work just as well for these applications.
You will want good paintbrush for spreading glue. I have a synthetic bristle brush I favor. The synthetic bristles seem to clean up more easily. When cleaning glue out, first remove as much as reasonable with a paper towel, then wash thoroughly, then leave it in a cup of water overnight. PVA glue is remarkably persistent. Minimize the amount you wash down drains, unless you're at a friend's house.
I use foam core board, decorative papers, heavier papers (I generally keep in stock a 70-80 pound paper, and a 130-150 pound paper), and scraps of wood 1/4 to 1/2 inch thick.
I have transitioned almost completely to using foam core board for wall mounting purposes. It's incredibly light, easy to cut, takes glue well, and is both stable and stiff. In the past I have used mounting board, which is really a double-weight mat board. This material is incredibly difficult to cut without some fairly robust tools, which I do not have. Wrestling this stuff down with an Exacto knife and a ruler is fairly tough sledding. If I want some sort of heavy mat board in future, I will likely cut standard weight mat board to size, and them laminate 2 or more layers up at the proper size with PVA glue. Mounting board and laminated mat board does have the advantage that you can sand it, with ordinary sandpaper, to create a clean edge. As we'll see my preferred methods tend to conceal that edge.
You're going to be using an increasingly glue-covered brush in this process. Plan where the brush gets put down, and always put it down there. Be mindful of the gluey brush end, and don't let it touch anything it's not supposed to touch. Have clean rags or paper towels handy to clean your fingers, and then clean your fingers obsessively. Be mindful of what has glue on it, and what does not. Keep the two separate, and have a plan for this. Perhaps you put some newspaper on the ground, and glue-covered scraps, rags, etc, get dropped on that? That sort of thing. Glue gets everywhere unless you're quite disciplined.
... to the Edge
In general I will glue prints out to the edge, to create a clean glued-down edge where the print meets the backing material (substrate). Holding the print carefully, back side up, run a small bead of PVA glue around the edge, and then a squiggle or X of glue in the center. Working fairly quickly from the inside out, brush the glue out to the edge, and spread it around in the center. You can tilt the print to see the glisten of glue, to ensure you're got the entire edge glued. You will likely find it hard to keep glue off your fingertips and thence the print, so practice a little.
You will almost certainly use too much glue the first few times. The glue bead shown below should be brushed out to the edge, but also into the interior, as it is a little too heavy:
Brush out toward the edge, to bring the glue all the way out:
Now turn the print over and position it carefully, one edge down first, laying the print gently down into position. PVA glue does not cure instantly, so you can reposition. Be ruthless about lifting and repositioning, it's OK. Once it is in position, gently lay a clean sheet of paper over the print and, working from the center outwards, press the print firmly down trying to work out any air bubbles under it. If you've used too much glue, it will squeeze out around the edges at this point. Regardless, assume your scrap paper has glue on it now, and dispose of it appropriately.
You will ruin some prints early on. You will probably ruin the occasional print later on as well, but less frequently.
This whole exercise is somewhat fraught, and altogether too often results in glue on the front of the print, so I really prefer to apply glue to the substrate rather than the print. This will result, however, either in glue appearing beyond the edge of the print, or in the print edges not being glued. Either must be dealt with.
I glue to the edge when the background material, the substrate, will extend beyond the print's edge, to create a matted look. This can be simply the white of the foam core, or you can dress it up a bit.
A design I employed once, as much to entertain my then five year old daughter as for any other reason, was to glue strips of decorative paper around on that mat area. I used a torn edge for the strips, and tacked them down with deliberate crudity (designs that embrace clumsiness are a boon when a 5 year old is helping you), and let the edge of the paper overlap both the edge of the substrate, and the print's area. I am still very pleased with this approach.
This is what it looks like. The whole thing is floated 1/2 an inch or so off the wall. The detail shows the print glued out to the edge, overlapping the strips of decorative paper, and also the wrinkled look of the paper. The torn edge is obtained by painting a narrow bead of water onto the paper, letting it soak, and then tearing along that weakened line.
There is, under the print, a bare rectangle of mounting board. The decorative paper in this case is four overlapping chunks of the same stuff, but there's no law you have to use the same paper on all four edges.
..."Floating" the bare print
I'm rather fond of the floating print look. Here I cut the substrate a little too small. 1/8 to 1/2 an inch too small in each dimension, depending on the look I am going for. If you want the print to float quite flat, you'll want the substrate very nearly the same size at the print, so cut it perhaps 1/8 inch too small each way.
Place the print face down on a clean, smooth, surface. Apply glue not to the print, but to the substrate, as indicated in the previous section for prints. You can be more careless, because the front surface of the print is safely face down and will remain that way, so a few glue-blots here and there will not be as big a deal. Position the substrate on the print, just as you positioned the print on the substrate in the previous method, being careful to let the print slop over the edges of the substrate very slightly.
This is part of an installation I made for my wife's office space. 13 small prints (4x6, 4x4) of our kids in an arabesque wrapping around her monitor. Total cost, under ten bucks.
Rear view of one of the prints. The print floats off the wall by the thickness of the foam core board, which itself rests against the wall:
For a somewhat different floating look, cut the substrate a bit smaller, 1/2 inch perhaps, in one or both dimensions. This will allow the print to curl. Do not bring the glue all the way out to the edge where you want to see some curling. After you position the substrate on the print, allow to cure completely (24 hours), and then gently curl the print up and away from the substrate. This creates a slight "scroll" flavor to the floating print.
This isn't a photograph, but the idea is the same. The whole is floated 1/2 an inch or so off the wall (see below):
I use two approaches. The first floats the whole assembled object off the wall by some distance, and consists of, essentially, just gluing wood scraps to the back of the piece. This is how all the pieces shown above which are floated 1/2 inch or more off the wall. The tulip photograph with decorative paper, and the Japanese print are both mounted this way. I use wood glue, and put a weight on the whole assembly for the glue curing time, but I see no reason PVA glue would not work just as well.
The upper block is simply rested on a nail driven into the wall. The lower block is merely a standoff, to make the print hang parallel to the wall. For more security, you can bevel the lower edge of the upper, supporting, block, to let it "hook over" the head of the nail. Here is a side view, with the blue outline indicating the wooden block and the green indicating the nail.
For a mount closer to the wall, especially with very small and hence light pictures, I simply pop a hole in the back of the foam core board, exactly half-way across the top. This hole is pressed over the head of a finishing nail (a common nail type that has nearly no head) driven into the wall and slightly protruding. As a final touch, I apply a dab or two of ordinary caulk to the bottom edge of the back, to give a little grip. Foam core board is quick slick, and the dried caulk's texture helps the print stay put on the wall. This is how the collection of small prints of my daughters is mounted.
For additional reinforcement (or if you botch the hole up) you can glue a piece of heavy paper over the hole. Use one of the finishing nails you'll be using in the wall later, punch a hole in the paper the right size to admit the head of the nail. Apply glue to the back of the paper, and slip it over the nail. Put the nail-head into the hole in the foam-core, and slide the gluey, sticky, paper in to place. The holes will be aligned by the nail, and will be the right sized to accept the nail's head.
And that's all there is to it!
No need to worry about museum glass versus anti-reflection glass or any of that.