Wash the hearth thoroughly before staining using a scrub brush and a solution of warm water and dish soap. Let the hearth dry.
Use masking tape to mask the edge of the fireplace door and any surrounding trim or attached fixtures.
Mix the stain solution in a plastic tub with a stir stick. Stain solutions are usually two-part systems that have a fixative and a pigment. Follow the particular manufacturer's instructions for acceptable ratios. Always test a little bit in an inconspicuous area and, if necessary, dilute with more fixative to lighten the stain or add more pigment to darken the stain.
Apply the stain using a paintbrush or a sponge that has the same width as the bricks. Paint in between the grout lines so that you are only coloring the bricks. Do not get the brush or sponge too wet so as to avoid drips. Have a wet rag handy to immediately wipe up any drips. Add a second coat after the first dries, if needed, to strengthen or even out the tint.