Sand the foam with 220 grit sand paper to create an even surface.
Mix equal amounts spackle and water putty in a bowl or bucket. Add water until the mixture achieves a paint-like consistency.
Paint the mixture over the surface of the foam to fill in crevices and produce a tough outer layer. Allow the mixture to dry for 24 hours.
Lightly sand the foam with 330 grit sandpaper. Paint the foam with acrylic paint as desired.
Cut cheesecloth into 1-inch thick strips.
Coat the cheesecloth strips with liquid latex, craft glue or a flour and water paste to make them sticky. For best results, use liquid latex for maximum flexibility on moving areas.
Spread the cheesecloth strips in a single layer over the foam. The dried glue and cheesecloth will create a sturdy surface. For added strength, allow the first layer to dry overnight and add additional layers of cheesecloth as needed.
Sand the final layer after the glue dries, using 330 grit sandpaper. Paint over the cheesecloth as desired, using a gesso primer followed by acrylic paint.