Choose the materials. Take accurate measurements of the room where you will be installing the flooring. This is a good exercise to help in ordering the proper amount of materials, and it is a good way to visualize the final design.
Check the subfloor for stability. The subfloor is critical to a good flooring installation. It needs to be at least 3/4" plywood. Particle board is not a good subfloor for hardwood and tile installation. If you have a particle board subfloor, remove it and replace with a 3/4" plywood.
Tape off a rough outline where the tile border will be installed. This will allow for accurate measurements, and center the tile design in the room. Remove shoe molding from around the room and install a vapor barrier paper, covering the entire floor surface and overlapping the strips at least 4 inches. Staple down securely to the subfloor.
Make a template for the tile border. In our design, the tile border is 7-1/2" wide, so we used 1"x8" boards and ripped them to a width of 7-3/4". (This allows for a 1/8" grout line along the inner tile line and the outer tile line.) Screw down the template to the sub-floor using drywall screws. Don't screw in the far end piece of the template at this point -- the hardwood planks will be nailed down and the lengths will be random so later a line can be marked on the boards and a fine cut can be made across the boards. Then the end piece of the template can be screwed down.
Cut a center board in the exact center to the template, aligning one edge with the chalk line that represents the exact center of the room.
Using a pneumatic nail gun, start at the center of the template and nail at least every 10 - 12". Keep the lengths of the boards random. Tap each board with a mallet to secure to the previous row and continue nailing until the first half of the template has been installed. Remove the center board in the template with a screw gun.
Glue a spine into the groove of the previous row of boards and continue the hardwood installation in the other direction. After all of the boards have been installed within the template, mark and saw off the excess boards for a nice finished edge. Screw down the last board on that end of the template.
Continue the hardwood installation for the rest of the room running the boards in the opposite direction using the same method of nailing. As you get close to the wall, there won't be enough clearance for the handle of the pneumatic nail gun, so it will be necessary to drill pilot holes into the planks and hand nail. Once there is not more clearance to drill pilot holes, face nail each board (nailing directly into the top of the boards) and set with a nail set and putty to cover the holes. After the hardwood installation is complete, remove the template from the floor.
For the Tile Border:
Mix a latex-based mortar and apply to the bottom of the template space. Cut 1/4" cement fiberboard with a scoring knife wide enough to fit snugly down into the template space. Screw down fiberboard with drywall screws.
Mix mortar with water to the consistency of cake batter. Let the mixed mortar sit for 10 to 15 minutes (this is called "slaking" and allows the moisture to be absorbed into any unmixed powder).
Using a 3/8"x1/4" U-notch trowel, apply the mortar directly onto the fiberboard, getting the mortar tight to the edges (image 1). Lay the first piece of tile border section into place. (The installation is quicker and easier to do if you plan your design around the length of the tile pieces without having to cut them.) Using a scrap piece of the hardwood flooring, gently tap down the tile border flush to the hardwood flooring (image 2). Repeat these steps until the entire tile border has been installed. Let the tile cure overnight.
Using a utility knife, scrape out any excess mortar that has collected in the tile grout lines and vacuum up the debris.
Mix grout using water to a consistency of peanut butter.
Apply grout directly onto the tile surface using a grout float and press down firmly into all of the joints. Cross diagonally with the tile, paying attention not to gouge the grout line with the edge of the grout float. Let the grout dry thoroughly.
Using a utility knife, pull out the grout between the tile and the wood (the inner grout line and the outer grout line). Pay close attention not to damage the wood with the knife blade. Vacuum up the debris.
Clean off excess grout using a wet sponge, drawing the sponge diagonally across the tile (the same way that the grout was applied). Rinse sponge out frequently until the entire surface is clean.