We learn the basics of colour mixing in elementary school---red and yellow make orange, blue and yellow make green, blue and red make purple. If you're learning how to paint, these basic rules of mixing primary colours become useful. Artist quality paints are expensive, and it's impractical to buy every colour you see. In fact, most art teachers will discourage students from buying many different colours, particularly black. Mixing your own paints creates truer and more natural colours.
Study the colour wheel. Find an image of a colour wheel online, and print it out. Or make your own colour wheel. A basic colour wheel will be the shape of a circle divided into 12 pie pieces. The three primary colours---red, yellow and blue---will be at three equally distant points on the circle. Between each primary colour will be a progression of secondary and tertiary colours. For example, three colour slices appear between red and blue. The centre colour is violet. Between red and violet is the colour red-violet and between violet and blue is blue-violet. The colours that are opposite each other on the colour wheel, like red and green, are complementary colours. They are opposites that when combined, create black.
Gather your supplies. To mix a variety of colours, all you need are red, blue, yellow and white paints. As you advance at mixing colours, you can try different shades. Colours come in warm and cool shades that change the mixed result. Some basic colours to start out with are titanium white, ultramarine blue, Prussian blue, thalo green, viridian green, yellow ochre, cadmium yellow, cadmium red and alizarin crimson. You also need paper towels for blotting, a palette and palette knife. If you are using acrylic paints, you can use water to rinse your brush. For oil paints, use a jar of artist's white spirit to clean the brushes.
Set up your palette. Squeeze out a quarter-size glob of a blue, red and yellow on your palette, spaced widely apart. Also squeeze out a slightly larger glob of white.
Start mixing the secondary colours. Do this by taking your palette knife, scooping up a bit of red and a bit of yellow, then mixing them. Notice how the amount of each paint you add changes the orange colour. Then mix the two other secondary colours, green and violet by mixing the other primary colours.
Once your secondary colours are mixed, try mixing tertiary colours. The tertiary colours are red-orange, yellow-orange, yellow-green, blue-green, blue-violet and red-violet. These colours are created by mixing a secondary colour, like violet, and a primary colour, like red, to create red-violet.
Now you can create different shades of the colours. On your palette, smear three small globs of each colour. Add a small amount of white to the first glob, and mix it. Then add a slightly larger amount of white to the second glob of that colour. Then add even more white to the third glob. Notice the different shades of lightness and darkness that you get out of each colour.
Create black by adding equal parts of complementary colours, like red and green. If the shade seems too warm, add some more green and vice versa. Then practice adding a bit of black to each of your mixed colours to make them darker.