For the fair ones, you are required to choose the browns which are warmer and can soften your skin color. And the browns include copper browns, honey ones and mahogany tones will be good choices.
However, these people with fair skin could not choose those colors which are overly dark. Because over dark colors will make your skin seem to be quite pale. If you cannot make your decision on the color of your hair, you may ask your barber for some advice.
For the medium ones, you should choose golden browns or chestnut which will highlight your skin color. When you are not sure whether the color is suitable for you, you may just find some pictures in the magazine or you may just color a small amount of your hair and see whether it looks good. You may also get some advice from the professional websites.
For the dark ones, you should avoid the mixed colors. You had better select the pure colors like pure white, woodsier browns and so on. Chocolate brown is also a wonderful choice for dark skin tones. If you want to make dark brunette better, you may use some bronze highlights to make your face look brighter and this will flatter your skin tones better.
Generally speaking, you should choose the right hair color according to the kinds of your skin tones, because different colors will create different effects on different skin tones. More often, if you color your hair in a proper way, your skin color will be complemented. However, you will also need to take good care of your hair. For example, you may use the shampoo that is specially designed for colored hair.