Lay two intersecting lines with your chalk snap-line, crossing at the center of the floor, so the room is divided into four squares. Lay a square at the intersection and adjust the second string as needed so the lines are perpendicular.
Spread thin set over the floor with a notched trowel, so it covers about three square feet in one of the corners of the intersecting lines.
Lay a black tile in the thin set at the intersection. Press a white tile next to it, putting two spacers between them.
Spread more mortar all around, and continue laying tiles off one another, alternating black and white. Build out toward the perimeter, using the lines to keep it all straight and continuing to alternate the two colors each time. Lay all the full tiles that will fit.
Cut tiles for the edges of the room as needed with a tile cutter, with each cut tile the opposite color of the last full tile in that course. Lay the cut tiles with the cut sides facing the walls.
Let the thin set dry for 10 hours. Pull out the spacers.
Spread grout over the floor with a grout float, forcing it into the lines and squeezing it off the surface. Wipe the residual grout with a damp sponge.