If you're painting Plexiglas, not just any paint will do. Some paint may not adhere well, if at all. Acrylic paints work best on Plexiglas, and spray paints designed for plastic work as well.
Preparation
Clean the Plexiglas with water and a mild soap such as liquid dish soap, rinsing it off thoroughly afterwards. If your goal is for the paint to adhere well, scuff it up with a fine-grit sandpaper; paint doesn't adhere well to slick surfaces, so the sanding gives the paint something to grip. Wipe the dust away afterwards with a soft cloth.
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Primer Perfection
A spray primer designed for plastic helps the paint adhere without cracking, peeling or flaking. Prime the side you wish to paint, placing the Plexiglas atop a plastic tarp or newspaper. Spray in even, overlapping bursts; then allow the primer to dry completely.
Warning
Work only in a well-ventilated area or outdoors when applying spray primers and paints to avoid breathing in fumes.
Painting the Plexi
Acrylic paint designed for art or crafts sticks to Plexiglas; once the material is primed, other paints such as spray acrylic enamels adhere as well. Brush or spray the paint on as desired; for a smooth look, use spray paints, as brushed-on acrylics may show the brush marks. Painted Plexiglas may still scratch easily, so apply a clear spray-on sealer over the paint, once it dries, for best results. If your goal is simply to create art on Plexiglas, using the material as your canvas, you can paint atop it after priming or directly after sanding and wiping it clean. Frame or display the finished work in a way so the Plexiglas will not be touched or scratched by other materials.