The easiest way to find color combinations is with a color wheel. The wheel should have at least 12 colors, giving you all the primary, secondary and tertiary colors. Secondary colors are those formed from primaries; tertiary colors are formed from a secondary plus a primary color.
With the wheel, you can easily pick out complimentary color combinations. Complimentary colors are those opposite each other on the wheel. One of the colors will serve as your main color, with the other serving as an accent. It's important to have an unequal representation of the two colors. Otherwise, instead of complimenting one another, they will clash.
Purple and yellow are opposite each other on the wheel and are, therefore, complimentary. You've seen this combination used to good effect in nature--think iris or purple pansy. Both are a rich, beautiful shade of purple with yellow markings that make the purple pop.
Next, look to the wheel to combinations that are almost opposites. For instance, the opposite of blue on the wheel is orange. One away from orange is yellow or some color that combines yellow and orange, depending on how many colors are in your wheel. Gold is a color related to both yellow and orange that tends toward the yellow. Rich cool blues look wonderful with gold, as you can recall from holiday decorations. Gold also works with certain reds for the same reason. You can also choose both colors lying on either side of the complimentary color. This is called a split complementary color scheme.
Analogous colors are colors laying next to each other on the wheel. Thus, red, red-violet and violet are analogous colors, as are yellow, yellow-green and green. Analogous colors are strongly related, so they harmonize together. (Think of a peacock feather.) A choice of analogous colors can be used alone or accented by the compliment of one of the colors in your range. An easy way to pick the accent is to choose the compliment of the middle color of your range. That way, the accent will be only one compliment away from the other two colors. For instance, jewel-toned violet, blue-violet and blue, plus gold (a relation to yellow-orange and compliment to blue-violet) works well. You don't have to choose just three colors, by the way. Even a swath of five or six colors might do. You'll know you've gone too far when colors no longer appear to work together.
A monochromatic scheme uses versions of one kind of hue, for instance, the whitest silver all the way through the darkest black. Choose a dominant tone from among the colors in the scheme. The very uniformity of monochromes, while soothing and even "zen," can be boring.
More advanced combinations are the triadic and tetradic color schemes, hard to pull off for beginners, but possible with the aid of a color wheel. With the triadic scheme, you choose three colors that are equidistant for one another on the wheel. If you drew a triangle linking the colors, it would be an equilateral triangle. Choose one of the three colors to be the dominant color.
The tetradic scheme uses two sets of complimentary colors. These form an X on the wheel. It is easiest to pull off when the X is narrow, say, using two colors for the bottom of the X that are only one color apart, with the resulting top of the X the same.
Choosing color combinations is complicated by such considerations as saturation, contrast, neutrality, warmth and coolness. Meanwhile, certain colors contain other colors that an untrained eye might not be aware of. For instance, a red might have a blue or orange cast.
To avoid problems, it helps to have concrete examples for reference. Such examples are handy to bring along when you are, say, visiting a store to pick colors for a room.
The outdoors, particularly gardens, are rife with usable color combinations. Take photographs in good light with a camera that creates crisp pictures.
Look to photographs in home and garden magazines. Those setting up the photograph are professionals trained to choose the best combinations of colors, shapes and texture. By saving photographs for future reference, you are essentially getting expert advice.
The same goes for artwork. Look to masterpieces. Often you can get postcards or small prints from museum shops.
Don't neglect fabric samples. Find a fabric warehouse that includes upholstery fabric. Such shops are a rich source of color combinations.
Finally, hardware and paint stores have many preprinted color strips.