Mark the dimensions of the backsplash on the wall that you want, using a pencil, level and square. Make the size of the area so it allows for use of all full subway tiles without any cuts.
Spread tile adhesive over the marked out area, using a notched trowel.
Set the bottom row of subway tiles in the adhesive, pressing them end to end over the whole span. Put spacers between the tiles, and under them, to separate them from the counter.
Set the first tile of the second course above the bottom course, at one end, putting spacers between the two courses and between the tiles of the second course. Arrange them in a grid pattern so the spaces between them are completely lined up.
Repeat, working your way up the wall course by course, keeping the grid pattern straight and spacing all the tiles. Cover the entire marked-out area.
Let the tiles set overnight. Pull out the spacers.
Spread grout over the tiles with a grout float, using the long edge of the float to press the grout into the spaces. Wipe up the excess grout with a damp sponge.
Let the grout set for 48 hours. Run a bead of caulk along the joint between the bottom of the tiled area and the countertop.