Clean the wood surface and allow it to completely dry. Use a notched mortar trowel to spread thinset mortar along one edge of the floor, covering enough area to lay one course of uncoupling membrane from end to end.
Set the first course of membrane in the mortar, pressing it firmly down. Cut it to size with a utility knife. Spread another row of mortar and set another course of membrane, pressed alongside the first one. Continue until the whole floor is covered in courses of membrane.
Divide the floor into four even sections, using a chalk snapline to lay two intersecting lines. Use a T-square at the intersection when you set the second line, to ensure that it is exactly square against the first line.
Spread thinset mortar over the middle of the floor, on top of the intersection of the lines, using your notched mortar trowel. Cover enough area to press four floor tiles into place. Set tiles in the mortar, at the intersection of the lines, putting spacers between them.
Spread additional mortar and lay additional tiles, building out from the center of the floor toward the walls, along the lines. Put spacers between all of them. Use the tile cutter to cut tiles at the edges of the floor, next to the walls.
Let the mortar dry overnight. Remove the spacers.
Grout the tiles with your grout trowel, using the long edge of it to press the grout into the tile spaces. Use a damp sponge to wipe off the surface of the tiles, leaving the grout between them. Let it set for two to three days.