Clean and vacuum the existing wood floor thoroughly.
Find the center of each wall. Snap a chalk line from the center of one wall to the center of the opposite wall, dividing the floor into quadrants. Hold the line taut about 1 inch from the floor, anchoring it at each wall. Pick the line up with your fingers and "snap" it, letting it fall to the floor. The chalk will transfer to the floor, making a straight line. This is your baseline for laying peel-and-stick carpet tiles.
Lay the first tile inside one quadrant, lining one corner up with the center point and its edges with the chalk lines.
Continue laying tiles along the chalk guidelines, creating a cross of carpet tiles and separating the room into quadrants.
Work on one quadrant at a time. One by one, lift up the carpet tiles you have laid out. Then remove the adhesive backing and affix them to the floor, carefully lining up the edge with the chalk guideline.
Fill in the rest of the quadrant with tiles. Cut the perimeter tiles to fit with a utility knife.
Apply carpet tiles to the remaining quadrants.