I shoot large format, and in a workshop this summer had an opportunity to use a "tray slosher" to develop film. I liked it so much i decided to build my own.
I bought some plexiglass (they call it 1/4'" but it's actually 0.22") at Home Depot. The guy in the orange apron suggested epoxy as the adhesive, but I knew better and went instead to a glass shop where I bought some plexiglass adhesive.
The key to working with plexiglass is to be very precise with the cuts. They must be absolutely square, and if you choose to sand the cut edges, make sure that you don't round them over in the process. When you are edge glueing this material, you want to be able to have one piece rest precisely on the adjoining piece.
Plexiglass adhesive usually comes in a glass bottle, and you have to purchase an applicator that is basically a syringe with a metal tip. Fill the syringe, and with the two pieces resting in the right position, carefully squirt a few drops of the adhesive along the seam between them. The adhesive will be drawn into the joint by capillary action - if you are using the clear version of the pliexiglass, you can actually see it filling the joint. Give it a couple of minutes to dry, and then go back to see if there are any gaps - if so, add a few more drops of the adhesive.
Do your glueing outdoors, and be careful with the adhesive. It evaporates rapidly, so keep the top on the bottle when you aren't actually filling the syringe, but it's not something that you want to breath the fumes from for an extended period.