One of the most well-known systems to find the right colors for you is the seasonal typology approach. This method can be quite helpful but it's still best to experiment yourself. You need: daylight, a mirror, the colored items from your wardrobe and the help of a friend whose judgment you trust doesn't hurt either. Try on your tops and scarves and see which colors work best for you i. e. enhance your natural skin tone. Usually you will find that you look best in either warm or cool colors. White, gray and black are considered neutral. I would also add beige and tan because they work with almost any other color.
After determining what colors work best close to your face you can start creating outfits:
Level One: Mixing 1 color with 1, 2 or 3 neutrals
For those who are drawn to all-in-black outfits it's quite easy. Simply add one dash of color by putting on a colored scarf or earrings or T-shirt etc. Are there any colors that don't work with black? The old rule used to be not to mix black & brown or black & navy but I don't think anyone really cares anymore, unless you work in a really conservative environment? Personally I'm not a fan of mixing brown and black leather.
When adding a second color to your outfit you could choose either an analogous or a complementary color couple. "Analogous color schemes use colors that are next to each other on the color wheel. [...They] are often found in nature and are harmonious and pleasing to the eye." Complementary colors lie on opposite ends of the color wheel like red & green, purple & yellow or blue & orange. These combinations are real attention-getters which is why they are so popular for sportswear. If you want to tone down a combination that might seem clashy use one of the colors as an accent. Red lipstick with a green sweater or a thin yellow patent belt with a purple dress.
"Analogous color schemes use colors that are next to each other on the color wheel. [...] "Choose one color to dominate, a second to support. The third color is used (along with black, white or gray) as an accent." For a more vibrant effect try the triadic color scheme or the split-complementary color scheme (to learn more about these please follow this link).
Schemes that use four colors work "best if you let one color be dominant. You should also pay attention to the balance between warm and cool colors in your design." Wear warm OR cool colors close to your face, whatever suits you best, for the most flattering effect and keep the colors from the opposite category for skirts, pants, shoes or bags. I think that the girl on the far left is a brilliant example of the use of a four color scheme. If you don't like to use that much color try a colorful accessory like the bag in the pic on the left.
The easiest concept to explain but maybe the most difficult to pull off depending on your self-confidence. Variations of this look in a dark shade can look quite elegant.
I think the key to successful color mixing is to be quite disciplined and really streamline your outfit until everything matches and nothing pops out (in a bad way). Of course this sometimes means that you have to buy a new item to pull a look together. If you're trying to save money, it is best to decide upon three colors (plus the neutrals) that work well together. This way it will be a lot easier to mix and match your clothes and will actually result in more outfit choices than having a closet full of colorful but hard to match items. For more inspiration I recommend these blogs: book of miri, Fruchtzwerg's Island, dreamecho and piksi's flickr photostream.