Draw the square or rectangular perimeter of the backsplash where you want it on the wall with a level and pencil. Adjust the size so it will use full tiles with no cuts.
Spread tile adhesive over the whole marked area with a notched trowel.
Set the bottom course of tiles into place in the adhesive, pressing them into the adhesive horizontally, running along the countertop. Put spacers between the tiles and the countertop, and between the ends of the tiles.
Press a second course of brick tiles in place above the first course. Stagger the positions of the tiles so the ends of every pair of tiles meet one another at the middle of the length of the tile below it. Put spacers between the tiles as you hang them. The tiles of the second course should jut out over the tiles on the first course at the two far sides of the backsplash area.
Repeat, building up the wall course by course, staggering each course off the one below it. Fill the whole marked area.
Let the adhesive set for 12 hours. Remove the spacers.
Spread grout over the brick tiles, scraping it across the face and pressing it into the spaces between. Wipe off the excess grout from the tiles with a damp sponge.
Let the grout dry for 24 hours. Run a bead of caulk along the joint where the bottom of the brick tiles meets the countertop.