Clean any loose dirt, dust and debris from the brick surface, using the masonry brush and vacuum cleaner.
Carefully add one bag of mortar mix to about one gallon of water in a 5-gallon bucket, while thoroughly mixing with the electric drill and mixing paddle. Read the mixing instructions on the mortar bag to ensure the proper mortar to water ratio.
Smear mortar on the back-side of a stone, with the brick trowel, and press it (the stone) to either end of the bottom edge of the fireplace wall. For best results, the space between the stone and the fireplace surface should be about 1/4-inch. Work your way along the bottom edge of the fireplace wall, using this process, until there is an entire row of stones. Cut stones to fit with the angle-grinder and masonry wheel, when necessary. Wear proper safety glasses when cutting stones, and read through the grinder owner's manual for any operation and safety directions.
Work your way up the fireplace wall, in horizontal rows, using this process until the desired height is achieved. Some types of stone may look best if the horizontal rows are uneven and random looking -- consult with a stone veneer specialist for best design results. For optimum mortar strength, allow the mortar to cure for about 24 hours before moving on to the next step.
Fill the grout bag with mortar, using the brick trowel as a scoop, and evenly apply the grout to the voids between stones if desired. Not all types of stone require the use of grout -- again, consult with a stone veneer specialist for best results. Clear any unwanted mortar from the stone surfaces, using a large wet sponge, and rinse with water as needed.