Install a cement backer board over the surface you are tiling. Cement backer board is sturdier than drywall, and will also smooth out an uneven surface. Attach the backer board to the surface with flat head masonry screws.

Cut the cement board when needed with a masonry blade.

Mix up a thinset mortar according to the directions.

Start at the bottom, if you are installing on a wall, or in the corner of a flat horizontal surface. Spread enough thinset for a few granite tiles with a notched trowel.

Place the granite tiles down so that they are next to each other. Leave no obvious gap. Repeat the thinset and placement for the first row, and then start the next. To make the lines between the tiles less obvious, you could stagger the rows so the seams aren't continuous across the surface.

Cut granite tiles with a wet saw so that the saw is cooled constantly. Use a diamond tip blade to cut through the hard material. Measure any places that your tile doesn't fit, and mark the back of the tile with the dimensions. Cut along the lines.

Let the tile sit for a day once you are finished.

Mix up a tinted grout that matches the color of the tile. Spread the grout over the tile to fill in the tiny cracks between the tile pieces. Wipe the tiles with a damp rag. Let the grout dry for a day.