Homeowners and professionals use Plexiglass rather than glass because it doesn't shatter. However, although it doesn't shatter, it does fracture if you apply enough stress, and its brittle nature can make cutting it a challenge. When you do cut Plexiglass, make sure you use the right tool.
Home Depot recommends the “score and snap” method. Clamp your sheet of Plexiglass between two pieces of wood so that the wood's edge marks the line you wish to cut. Cut the line using a score knife, preferably one with a tungsten carbide tip. Turn the glass over, and score the other side of the glass along the same line. Then unclamp the wood and snap the glass in two using your hands. The problem with this score and snap method is that Plexiglass lacks a defined crystal structure. The glass will likely break if you don't cut it correctly. To avoid cracking it along any line but your cutting route, make sure you apply significant pressure throughout the process, and do not vary this pressure at any point. Also, only score and snap along straight edges.
When dealing with larger pieces of Plexiglass, it's almost impossible to manually apply even pressure along the entire pane. Use an electrical tool. A table saw cuts straight lines particularly well, but a jigsaw costs less, and you can store it more easily. Use a variable speed jigsaw, and practice on scrap Plexiglass until you determine the correct speed. If the glass cracks randomly, increase the speed. If it melts, reduce the speed. Use an unpainted blade, because coated blades create friction that can melt the glass. Trial and error can help you find the perfect blade, but 32-teeth-per-inch blades usually work well. Wait till the saw has fully sped up to the speed you've chosen before touching it to the Plexiglass.
You normally want to avoid melting the Plexiglass with your electric tool because you prefer a clean cut to an uneven edge. But if you slowly melt the glass using a soldering iron, you can cut cleanly using the iron's sharp point. Plexiglass melts at 320 degrees F, and soldering irons get hotter than 700 degrees F. Plug in your iron till it heats up fully. Cut your Plexiglass along either a straight edge you've lined with wood or a curved line you've drawn with a wax pencil. The real advantage with a soldering iron is that you can cut any shape without fearing the glass cracking. The process is extremely slow, though, so use this for small intricate work rather than larger jobs.