Across the top of the color charter you will see a palette of ten colors. These are essentially paint brushes that you can color the chart with.
The color on these brushes can be changed by clicking the "Change Colors" link to the right. Now, clicking on a color in the palette opens a rectangular color wheel below it. Pick the color you want from the wheel and the palette color will change to it. This will also change every square in the chart that was drawn with that color, so if you want a new color and want to keep the existing one, use a brush you haven't drawn with.
Notice the vertical bar to the right of the color wheel? That's the brightness bar. Click on it or slide the arrow beside it up and down to change the brightness of the color you've chosen.
You can also use the color picker to change the colors on an existing design without changing the pattern.