Scrub the concrete sidewalk with a solution of ½ cup trisodium phosphate and a bucket full of warm water. Rinse off the solution with a hose.
Fill any holes, pits or cracks in the sidewalk with a concrete patch compound and a putty knife. Spread the compound around the surface of the patch with a trowel to even it out, known as "feathering". (see ref 1)
Place the slate tiles or pieces on the sidewalk and create a pattern. Place the thickest pieces near each other as these will require less mortar than thin pieces. Mark the back or rough side of the slate in the order you want to lay them in.
Use a ½ inch notched trowel to spread thinset mortar over one end of the sidewalk, spreading enough to set three pieces of slate at a time.
Add a small amount of mortar over the first piece of slate and press it into the surface. If you're laying slate tiles, place spacers at the corners of each piece. Lay a straight-edge over the tiles and apply equal pressure to make the pieces even with each other. Continue to set the slate in sections of three at a time.
Make a thick, pasty batch of grout using sandless grout mix and water so you don't scratch the slate.
File the spaces between the slate with grout using a grout float to press it down. Go over each section with a wet sponge to prevent grout stains. Wait about two days before using the sidewalk.