Tile is best installed over a hard, immobile surface, such as concrete or cement-board, but that doesn't always work out. Sometimes you'll want to lay the tiles directly over an existing particle board subfloor because you don't want to raise the level of the floor by installing backboard. Don't ever lay tile this way in a bathroom or other wet room, as the particle board will absorb moisture and cause tile cracking. Proper securing and preparation of the particle board is crucial, and using thick tiles will help.
Step around every section of the particle board floor, slowly, looking for any movement or loose spots. Use your drill to sink a 1 1/2 inch galvanised screw anywhere you find movement. Pay special attention to the seams between the boards. Make sure to sink the heads of the screws.
Use a chalk snapline to divide the floor into four square sections, with two intersecting lines running from the middle of one side of the floor to the middle of the side across from it. Before you snap the second line, use your T-square to adjust it to 90 degrees with the first line.
Use your paint floor roller to lay a thin, even coat of sealing primer over the whole particle board surface, starting from the farthest corner of the room and working your way out. Let it dry for a day.
Spread thin-set mortar in the particle board at the middle of the floor using your notched trowel. Cover the area over the intersection of the two lines with enough mortar to encompass more than four floor tiles. (You'll still be able to see the chalk lines through the mortar.)
Set your first four thick floor tiles into place at the intersection. Put tile spacers between them as you lay them.
Repeat the process over the rest of the floor, spreading mortar and setting tiles. Use the lines to keep a straight grid pattern out toward the walls. Put spacers between all the tiles as you lay them. Use your tile cutter to trim the tiles at the edges of the floor.
Let the tiles set for a day. Remove the spacers.
Spread grout over the tiles with a grout float, pressing the grout into the spaces between the tiles. Wipe up excess grout with a damp sponge. Let the grout set for at least two days.
Wear goggles when using the tile cutter.