Set up an A-frame ladder underneath your Styrofoam ceiling.
Remove the ceiling tiles. Styrofoam pieces are usually not attached to the ceiling frame in any way. The ceiling tiles are removable by lifting them upward then twisting the panel until it fits through the open hole. Reposition the ladder as necessary to comfortably reach each tile. Don't risk leaning off the side of the ladder to reach a section of the ceiling.
Place the panels face-up on a large plastic sheet.
Roll acrylic emulsion paint onto the panels with a medium-nap roller. Acrylic emulsion paints are available at some hardware stores and almost all art supply stores. Emulsion paints with acrylic resin are safe for use on Styrofoam. Other paints damage Styrofoam surfaces.
Apply a second coat if necessary after two hours. Acrylic emulsion paint often covers in just one coat, but you may need an extra one if there are any bare patches.
Reinstall the Styrofoam ceiling tiles after the final coat of paint has dried for 24 hours.