Polystyrene offers many advantages as a material for arts and crafts projects. It is relatively inexpensive, relatively light and very versatile; however, one disadvantage is that polystyrene tends to melt when exposed to solvents, like those found in many common paint brands. Water-based paints, such as acrylics and latex house paints, will not cause the polystyrene to deteriorate.
Acrylic craft paints are not solvent-based so they are safe to use on polystyrene. They are widely available in craft stores. The amount of paint needed for full coverage will vary from piece to piece, depending on how rough the surface is. Two or more coats may be required. Small pieces can be painted a solid colour by placing them into a bag with some paint and turning the bag so they become coated. The pieces can then be removed with a toothpick.
Spray paint is not usually recommended for painting polystyrene. Most of the common brands of spray paint are solvent-based and will melt the polystyrene if applied. Water-based spray paint is safe to use on polystyrene. However, the propellant used can still cause the polystyrene to melt if it contacts the surface. Follow the manufacturer's directions regarding the correct distance from the surface at which to hold the can.
Latex house paint is another option for painting polystyrene. A brush should be used for any detailed work, but rollers are useful when painting large pieces a solid colour. Multiple coats may be needed to ensure optimal coverage. Completely painting the piece in one or more thick coats will also have the effect of sealing and protect the polystyrene. Solvent-based paints could be safely applied at this point.
Sealing or coating polystyrene in some other material allows the use of any kind of paint, even that containing solvents. Polystyrene can be sealed with commercial finishing agent that can be purchased from hobby and craft stores. It can also be sealed with liberal applications of water-based paint or white glue mixed with water. Test any sealing methods on small piece of scrap foam before applying them to a project.