Sand painted pressboard to scuff the finish, and wipe with a tack cloth.
Apply a waterproofing primer according to the instructions on the can. Don't use a paint primer -- use one specifically made for tile substrates. Allow to dry.
Mix your mastic according to package instructions, and apply a skim coat to the pressboard with a trowel. Scoop additional mastic onto the surface and spread with the toothed side of the trowel.
Lay your tile onto the mastic, applying additional mastic to the backs of tiles that are very heavy or larger than 4 inches. Press into place with a clean grout float, and place spacers around the edges if necessary. Repeat, butting each new tile against the spacers of the last one, until all tile is laid.
Clean mastic from tile surfaces with a barely-damp sponge, and allow to dry overnight.
Mix tile grout according to package directions. Apply to tile with a clean grout float, pressing into spaces as you spread. After spreading a small area, hold the float at a 45-degree angle to scrape away excess. Continue until all the tile has been grouted. Allow to dry for 15 minutes.
Wipe tile with a damp tile sponge, using circular motions to remove excess grout from the surface. If you notice grout coming out from the grout lines, let it dry for a few more minutes and try again. Allow to dry.
Wipe the tile again, using the smooth side of the sponge to smooth the grout lines. Allow to dry.
Continue to wipe the tile periodically until the grout lines are clean, neat and the proper size. Allow to dry.
Wipe the surface of the tile with balled-up cheesecloth to remove haze. Allow to cure for 72 hours, then apply grout sealer according to instructions on the bottle.