If you want to learn the basics of mixing paint colors and how different colors are created, this tutorial is a good place to start.
If you study a basic paint color mixing chart, you will see that it all starts with the 3 primary colors - yellow, red and blue. By mixing these 3 primary colors in varying proportions, you get different colors that can also be mixed together... to produce more colors that can be mixed yet again...
The deeper you go, and the more paint colors you combine, the more complex and moody the color becomes. If you keep going, you will arrive at a neutral gray or black at the end.
Even just by mixing paint colors in different amounts, you will get hundreds of color variations, but it doesn't stop there. Virtually any color can be extended even further, by turning it into a shade, tint or a tone.
If you add white to any color, that color becomes a tint. You can add just a tiny bit of white, or a lot of white, to create dozens of tints of any particular color. For example, if you start with pure red, and gradually add white to it, can you see how many color variations you can get out of it before it becomes white? Yep, a whole lot!
Another way to extend a color is to turn it into a shade, by adding black to it. Again, you can create dozens of shades of any given color before it turns completely black. If you take red and add different amounts of black to it, you will produce shades ranging from a deep red to deep brown. Experiment and see for yourself.
When you add gray to a color, you create a tone. Mixing paint colors with gray is the way to go when you need to neutralize a color, and make it less saturated. Gray (when used in the same value as the color it is added to) does not make a color either lighter or darker - it simply makes it less intense.
Another way to neutralize a color and reduce its intensity is to combine it with its complement. For example, if you wanted to make a green color less vivid, you would add a little red to it (red and green are complements - see the paint color wheel). The more complement you add, the duller the color will become. If you mix any 2 complements in equal amounts, you will get a flat gray.
To increase the intensity of a color, you simply add more of the pure color to the mix.
Mixing paint colors is a fun thing to learn, but it's best learned from doing, not just reading about it! So get your paints and brushes ready and start playing!