Sweep up any dust and other debris from the floor. If the floor is particularly dusty, clean it with a wet mop. Do not use any soaps or solvents because they may interfere with the adhesive. Allow the floor to dry.
Use a carpenter's chalk line to divide the floor into quadrants and find the center of the floor. Use a tape measure to find the centers of the walls and mark them off. Stretch the chalk line from the center of one wall to the opposite wall and snap to make a line. Repeat for the other pair of walls for a total of two lines intersecting to make a cross. For even further accuracy in placing the tiles, snap a diagonal line from one corner to the other in both directions.
Go to the center of the room and place a single tile down along one of the lines so that two edges of the tile are flush with two of the lines. Lay down three more tiles to make a square. Work your way out to the walls until the floor is completely covered. Cut any tiles down to make them fit at the edges if necessary. Use a carpenter's square and a utility knife to ensure that you have straight lines.
Inspect the nap of the tiles. Make sure it is all going the same way or arrange the tiles in a pleasing pattern. Lift the tiles up from the floor and stack them in piles when you are satisfied with the arrangement. Leave the cut tiles stacked up near the walls.
Spray, roll or brush a thin layer of adhesive on the floor at the center of the room. How you apply the adhesive depends on the type you use. Read the instructions on the packaging. Apply enough adhesive to lay two to four tiles at a time, but spread enough adhesive to cover one and a half times the area of the tiles you are laying so there is some overlap. This is to prevent accidentally painting adhesive onto the tiles.
Press the tile down firmly and flatten out any bubbles or wrinkles. Work slowly to make sure the pattern is the same as you had it before. When you run out of floor to keep your materials on, lay down some painter's plastic to protect the tiles from spills. Use a 70- to 100-lb. carpet roller to press the carpet down onto the adhesive for a tight seal. Let the adhesive cure for the recommended time as directed on the packaging.