Ah, okay. This may be long.
Basically, there are many, many ways to digitally colour, right from simple 'block-in' to actual painting. Much of the learning process comes down to experimentation and study. This is, of course, a long term process. Sakura is right in that. I have been serious about art for, what, 7-8 years now. I only started digital art about 3 years ago but I had a fairly solid understanding in the traditional arts by that point. There is no difference between digital art and traditional art when it comes to theory, only in practice. Colour theory, study on form and shape, anatomy, these are all the same. Try to do some searching on the internet for overall tutorials on understanding light and colour, like this one
http://www.itchstudios.com/psg/art_tut.htm . This is not really something you can skip over if you want to be good. I highly recommend practising on stuff that you like, your characters and stories, by try to study at the same time. If you don't understand something, go read up about it and then apply it to your work. You will eventually see massive improvement.
As for technical advice, well that depends what you feel comfortable with. There is no wrong or right answers, only what works. In that, both Greeny and Alera are right. What Greeny is describing is a very basic way of cell-shading. The colours are not particularly exciting and they may not be correct. HOWEVER, it does get the job done and can provide a clean and stylistic look. I do not tend to use black to shade though because I believe it muddies the colours. I like to use a light purple, that when set to multiply, casts a nice purple shadow. These are examples of when I have used the process of a multiply layer on a low opacity setting to shade:
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As you may have noticed, some of the shading edges are soft. For this I simply painted the shadows using a hard edged brush (or you may use the selection tool) and then I used a soft edged eraser to soften the edges of bits. Some things should be softer then others. Simple, clean and efficient.
White can be used for highlights, but technically only when pure light would be reflected, such as metallic objects. However, when doing cartoon drawings, you can sufficiently break the rules as long as the message gets across. When shading non-shiny objects, like clothing, white being used as a highlight cab be a bit weird. Again it is best to study real life as well as the works of others to figure out what you like and what you can do.
I won't say you are restricted by the tools you use, since technically that isn't true, but I never personally figured out how to paint digitally with a mouse. I doubt I would be able to produce something like this with a mouse,
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but I have seen some people work wonders. I use a wacom tablet, which is expensive but the time it saves and the control it gives me is worth every cent in my opinion. Brushes really come into their own when you use a tablet since you can use pen pressure. Without a tablet, the selection tool is probably the best to use in the beginning, though continue to try out the brushes since you will learn as you go.
All of this is pretty general advice of course. Do you have an example of the colouring style you would LIKE to achieve? I could give you much more comprehensive technical advice if you had something in mind.