There is surprisingly little information on the 'net regarding acrylic joinery. Gluing two pieces of acrylic is a common operation for many hobbyists and craftspeople, but it seems the only forums that deal with acrylic are those that attract custom aquarium builders. Those projects are often very large and use slightly different techniques than what would be used for small projects. I had to search for a long time and still came up with relatively little info, so I would like to share my experiences.
There are a handful of different general methods that can be used two join one acrylic edge to the surface of another piece. I have tried a few, and think that the "pins method" is definitely the easiest and most reliable. In this method, one piece of acrylic is supported on its edge by a series of pins, spaced about 6 inches apart, above the face of another piece of acrylic. The solvent is applied to the gap and allowed to soften the acrylic for about 30 seconds. The pins are then removed, and the top piece is lowered onto the bottom piece. The joint must be supported for a few minutes until it is strong enough to hold the weight of the piece. The result is usually very good, and the operation can be controlled by using pins of different diameters, and letting the solvent soften the pieces for more or less time.
Step 1: The most critical step is edge preparation. The edge of the acrylic must be extremely flat and smooth. My favorite tools to achieve this in order of preference: 1. Jointer 2. Router 3. Table saw with high-quality blade 4. sanding. I would only recommend sanding if you are preparing the face of a box or the end of a large-diameter acrylic tube. Sanding is usually extremely slow, and does not work at all if you are trying to hand-hold a single sheet of acrylic at 90* to the sandpaper. If sanding is necessary, use a large sheet of glass with sandpaper attached to it with double-sided tape. Push the part back and forth over the sandpaper, and move up through the grits. The glass will make sure the surface is as flat as possible. Generally, water is used with grits 320 and higher, and I would say 320 is as fine as the surface needs to be. I would not recommend a power sander because the are hard to control, usually do not cover the whole surface of the part, and tend to overheat the acrylic.
Step 2: Position the parts with a jig or a square. It's important to position the parts so that the bottom piece extends 1/32" to 1/16" past the outer edge of the top piece. This will hold the excess solvent and will make life easier because the excess can be cut away with a router flush-cut bit later.
Step 3: Insert pins between the bottom and top pieces every six inches. Sewing pins are usually too fat. I like to use short pieces of solid copper wire that measure .015" dia. If the pins are too fat, when you remove them there will be a lot of excess solvent that spills out and it will make a mess.
Step 4. Fill the gap with solvent. Use a standard "hypo applicator" or "needle bottle". Squeeze the bottle while it is upright, then tip it upside-down while loosening your grip on the bottle. It will suck in some air, and prevent the solvent from coming out until you want it to.
Step 5. Remove the pins and let the top piece rest on the lower. Do NOT use any force to push the top piece down. As soon as the top piece is positioned correctly, let it sit completely undisturbed for 5 or 10 minutes.
You can handle the piece very carefully after 10 or 20 minutes (depending on the temperature) and continue with other glue joints in the project. Full-strength usually takes 2 to 4 days. The joint will initially look a little 'textured', however the optical clarity will improve over the next 24 hours. Of course, air-bubbles will never go away, so you can decide right away if the joint is not good enough in that respect.
After a lot of experimenting, I found out that the brand of acrylic and the brand of solvent make a HUGE difference in the quality of the joint. Check out this page which shows a grid of comparisons: