Prepare the wall. Install thin brick on a concrete or concrete block wall indoors with mortar, just as with an exterior façade. Prepare a wall with wood sheathing or drywall one of two ways, with cement fiber backerboard or metal lath. Use drywall screws driven with a screw gun into studs to secure the cement backerboard, typically about 1/4-inch thick, or put metal lath over a moisture barrier stapled to the wall with a construction stapler; fasten the lath with galvanized nails driven with a hammer into wall studs.
Spread a "scratch" coat of mortar over lath. Use a rectangular mason's trowel to put about 1/8-inch of mortar over the lath. Scratch it with the notched edge of the trowel, a stiff bristle broom or a leaf rake to roughen the surface. Let that scratch coat dry overnight. Backerboard is a cement product and needs no scratch coat.
Measure up the wall from the floor with a tape measure 6 or 8 inches at each end of the wall and snap a level chalk line between the points as a guide to keep brick lines level. Spread thin-set mortar or mastic, depending on the recommendations of the thin brick supplier, on the backs of bricks with a trowel and set them in place on the metal lath or backeboard. Press the bricks firmly into place until they are secure.
Leave joint gaps between the bricks; use plastic tile spacers if necessary to keep joints even. Lay a bottom course first. Use a level to keep bricks level. Start the second course with a half brick; cut a brick in half with a masonry blade on a circular saw. Add bricks to the end of the wall, start the third course with a full brick, the next with a half-brick, repeating until the wall is covered.
Grout the joints after the mortar or mastic dries; remove the tile spacers if you used them. Fill a fabric grout bag fitted with a metal tip with wet grout. Squeeze the bag to force the grout into all the joints between bricks. Don't overfill the joints, and wipe off any spilled grout with a damp cloth. Finish grout joints with a tuckpointing tool or brick finishing tool to make them smooth and even with the brick surface or slightly below it.