Begin with a sketch of the prop you are going to make. Understand how big it needs to be with the correct measurements and proportions.
Cut down a large piece of foam to a basic shape using the electric knife. Common foams used are sheet foam, Styrofoam, urethane foam or ethafoam. The basic shape must be just a bit larger than the final prop.
Systematically shave off corners and edges a little bit at a time to work toward the final shape. Shave off only a little bit at a time, very carefully or you can quickly lose proportion.
Use small knives to work in the final detail once you have the correct shape. This includes carving patterns and decorative designs into the prop for design purposes, making the prop look historically accurate or conducive to the scenic design of the entire play.
Coat the 3D foam prop with a non-toxic and water-based foam coat when the carving is finished. This seals in the foam so that it does not break easily nor shed foam particles, and so the surface can be painted and treated.
Allow the foam coat to dry completely--generally overnight. Use acrylic paints to color the foam prop. Texture it to make it look worn and aged with white and gray paints.