Install at least two layers of 3/4-inch-thick plywood material to act as a subfloor on top of your existing porch. Screw the first layer down, and install the second layer on top of the first, off-setting the second layer such that it doesn’t line up with the first. Make any necessary cuts with a circular saw.
Put down a layer of underlayment on top of the subfloor. Measure with a tape measure and pencil, and cut the pieces of underlayment to fit. Mix some mortar in a bucket with the drill and paddle. Spread a layer of thinset mortar onto the subfloor with a 1/8-inch notched trowel, and install the pieces of underlayment on top of that. Nail them in with the nail gun every 4 inches.
Measure out from the longest wall the distance of two tiles including a grout joint (or the equivalent of roughly 2 feet). Mark that measurement at both ends of the wall on the floor. Snap a chalk line between those two marks. Measure back the same distance from one of the perpendicular walls where you want to start with full slate tiles. Mark that measurement along the existing chalk line.
Use the framing square to draw a square line perpendicular to the chalk line. Snap a second chalk line across the first, so you have two perpendicular lines. Use the two-tile measurement to snap 2-by-2-foot grids across the entire surface of the porch. Mark the width of two tiles out from your existing chalk line, and snap the line. Repeat the process for all lines.
Mix a new batch of thinset mortar in your bucket with the drill and paddle. Spread a layer of thinset mortar onto the floor into one of your grids with your notched trowel. Set the slate tiles into the thinset. Work your way from grid to grid. Make any cuts needed with the tile wet saw. Allow the installation to set for 24 hours before grouting.
Mix some grout in the bucket. Spread the grout into the joints between the tiles. Wait 20 minutes for the grout to set up. Fill the bucket with water. Use a damp sponge to smooth the joints clean and to wipe excess grout from the face of the slate. Wait at least 72 hours before using the porch.