I have done a checkerboard pattern before and it can be a pain in the but! It takes more time and more patience, and really needs a second person to help lay out the tape correctly. I hope this helps.
Paint the entire area white first. Since white is so light, it may take multiple coats to achieve the right shade (depending on the product you use.) Then use a "double tape technique" to achieve the pattern. This is two pieces of tape laid side by side next to the center line of each sqaure.
Begin by locating the center point of the front, rear and side walls then marking that point accurately. Measure the preferred checker size dimension, in your case a three foot length for a 3’x3’ along each wall, marking from the center points and continue marking from both sides of the center point along the entire length of each wall. Begin taping your first set of two parallel lengths of masking tape tightly on either side of the markings at the walls and run your masking tape, holding one end to the floor and unrolling the elevated tape across the floor to the point directly opposite. Press the tape firmly into position. Continue this for each point until completed. To get a sharp corner, trim with a sharp razor knife. Cut away the tape from the inside of every other square and paint with black. I would recoomend a clear top coat as well. It takes time and effort, but this way the squares turn out well and have sharp edges.
A couple of things to consider- Use a high quality low tack masking tape- the job can be ruined by the wrong/cheap tape. CAREFULLY remove the tape! Pull at a 45* angle and do it slowly, keeping the razor knife on hand to score any stubborn tape. Reserve some of each color of the material for any touch ups, which seem to always be needed when removing tape, as some material may come up. Be patient! Low and slow and steady as she goes!

Good Luck!