There are two basic color wheels:
The first image is the usual color wheel (generated by Red, Blue and Yellow). The second is the light color wheel (generated by Red, Blue, and Green lights). There are three different types of colors on the chart: Primary, Secondary, and Tertiary. I have only labeled the Primary and Secondary colors on both charts. (That means anything without a label is a Tertiary color).
Choosing 1 color is easy! You can just pick a color or shades of one color. One of the prettiest Temari balls I saw was completely 1 color (not even shades!).
Choose 2 colors in lots of ways! You can choose adjacent colors or you can choose opposite. Again, you can work in shades of a color or not -- you're choice.
Choosing 3 colors is easier than you think. Just think of an equilateral triangle drawn with it's center over the center. And you have picked out 3 complementary colors! (For example: Red, Blue, and Yellow) (Another example: Orange, Green, Purple). You can also use just 2 of these 3 colors!
There are other color wheels you can make as well (just start with 3 basic colors). This page is meant only to inspire you, and not as a requisite.