If you have a jigsaw, you can cut Plexiglas. One trick to help prevent splintering is to stick painter's tape over the cut line. To keep the saw from veering left or right on straight cuts, use a clamp-on guide. This will give you a more professional look. Also, don't forget the blade: Find an uncoated (that is, unpainted) fine-toothed sheet metal jigsaw blade (such as DeWalt's 32 TPI). It might be a good idea to practice first on a few scrap pieces of Plexiglas.
Place the Plexiglas sheet on an even work bench or table.
Use a yard stick or ruler to roughly measure the length of Plexiglas you wish to cut. Mark your cut line with a grease pen.
Cover the cut line by sticking a line of wide painter's tape directly over it.
Measure again and mark another cut line atop the painter's tape.
Snap the jigsaw's plastic base and insert into place.
Put on your safety goggles, leather gloves, ear plugs and mask.
Place the blade of the jigsaw at the edge of the cutting line.
Turn on the jigsaw and slowly cut the first few centimeters of the Plexiglas. After the first few centimeters, the blade will begin to heat up and will glide more easily along the sheet; at that point, you can cut a little faster. When you near the end of the cut, grab the overhanging section of Plexiglas before it falls. Do not put your hand near the blade.