Plexiglass is some what a challange to work with. I used to do protoype stuff, real simple things, in a machine shop for a while. You can cut it with a regular circular saw/hand saw/milling machine. The trick is to keep from scratching up the rest of the piece, and most plexi comes coated on both sides with a paper adhesive combo. You have to be careful not to melt the plexi if your using power tools, and always over cut the piece, you can sand or file to the right size.
To finish the cuts, you have to sand them down progressively with wet/dry sand paper and polish them by hand (not recommended) or with a slow speed buffer (drill) and appropriate polishing compound. Or, you can flame polish with a clean burning fuel like butane or propane. Trust me, this is tough and you can ruin plastic easy. The concept is to "melt" the roughness smooth, but dont try it with a rough cut piece.
Connecting plexi is a whole other story, If you plan on using screws you have to pre-drill everything properly, and dont overtighten them or you will crack/break the piece. Best bet is to drill and tap and use real machine screws, not wood screws
Another option is someing like PVC cement but its a special solvent that acts very quick and finishes clear. I forget what the stuff is called but it smells similar to acetone. The way you use this is to get all your joints as close fitting as possible clamp the snot out of them and just let the solvent seep into the joint thru capilary action. One bad thing about this stuff is there is NO room for error. Any excess will drip and mark/ruin your part. And once the piece is joined there is no turning back.
If you plan to try this, do your homework, its tough...good luck tho.
Oh yeah, one more thing. Dont use pop rivets, it stresses the platic too much and may crack/break