Measure out the space where you want the stone. Cut plywood to the size and shape for your faux stone installation. Keep back at least four inches on every side of the fireplace for safety.
Paint the plywood with gray paint so that it will show between the stones and look like mortar. Wait for the paint to dry. Screw the plywood to the wall. If you are installing over plaster, sink the screws into studs. If you are installing over brick, space the screws evenly and use masonry screws.
Make forms for the faux rock using disposable containers of various shapes and sizes. Look for shapes that will mimic natural stone. For example, dent a paper bowl in a couple places to give it a more irregular, natural look. Line the forms with plastic wrap and secure them with duct tape.
Mix a small amount of the two component expanding foam according to the manufacturer's instructions, wearing gloves. Pour the mixture into a mold to see how far it expands. Note the amount you mixed and how far it expanded. Wait for the foam to cure per the manufacturer's instructions then pop it out of the form. Re-line the form with plastic wrap if necessary.
Calculate the amount of liquid necessary to fill all the forms you've made. Mix the components and fill all your forms in one step. Set the forms up on a tarp so you will be able to reach all of them in rapid succession. Wait for the faux rocks to cure and remove them from the molds. Repeat until you have enough stones for the fireplace.
Paint the foam to look like stones using textured paint and stone colors (see Resources). Vary the texture and color to create a natural appearance. Let the stones dry.
Glue the stones to the plywood leaving a regular space between them so the gray paint will show through and suggest the appearance of mortar between the stones.