Lay your first piece of cement board starting in a corner of the room. Use your notched trowel to spread mortar adhesive over the area where the cementboard will go. Press the board down into the adhesive. Use your screwgun to sink drywall screws every six inches. Repeat the process for the rest of the cement board, laying the pieces end-to-end and staggering them between rows so there are no four-way intersections. Where cuts are necessary, use your razor knife, scoring the board and then snapping it.
Tape between the joints of the cement board by spreading mortar adhesive along the line with your wide putty knife, laying a strip of mesh tape along it, spreading another layer of mortar adhesive over the tape, and smoothing it out with the putty knife. Let dry overnight.
Use your chalk line to lay two lines across the center of the room in each direction, intersecting in the middle, so you have four sections. Working one section at a time and starting from the middle of the room, spread tile adhesive with your notched trowel and lay your tiles starting along the snapped lines. Put tile spacers between the tiles at the corners. Continue until no more full tiles will fit at the edges of the room.
Let the tile set for a few hours. Remove the tile spacers by popping them out with your putty knife. Cut and lay the tiles at the edges of the room, scoring them on your tile cutter and using the prongs on the cutter to snap them as scored.
After the floor has set for a day, mix your grout according to the instructions and spread it over the floor with your rubber trowel, pressing it into the crevices between tiles and squeezing it off the tile face. Let it sit for two or three minutes, then wipe it all down with a wet sponge. Let the grout set for a day before using the floor.