Here's how I did it.
First, cut two colors of fabric (I used white and blue) into 5" squares.
Lay one of each color on top of the other with the "pretty" sides facing in. Pin around the edge.
Sew all the way around the square, removing the pins as you go. You can do this with a sewing machine, but since I don't have one, I just did tiny stitches by hand all the way around.
Once you've sewn the two pieces together, cut your square into 4 triangles on each diagonal using your ruler and rotary cutter.
Once cut, open the triangles (you should now have squares) and iron them so they stay flat. Make sure the back seam stays to the darker color's side so it can't be seen through the white.
Now that you've got your two-tone squares, rearrange them so they form a pinwheel.
Now it's time to sew the pinwheel together!
Take one square, and "fold" it on top of the one beside it so it's facing down. Line up your seams on the side that should touch and pin along the edge. Once you've sewn along the pinned edge, open it up and iron so it stays flat. Do this with each half of your soon-to-be pinwheel.
Just one more piece to sew! Now lay one side on top of the other, line up the seams, and pin along the edge again. Once this is sewn and ironed, you'll have completed your first pinwheel!