The Wikipedia article on normalization is reasonably good:
http://en.wikipedia.org/wiki/Database_normalization
Follow the links to the various normal forms. There's quite a lot of formal language in there, which may seem a little daunting at first sight, but try and get your teeth around it as once you have an understanding of these formal principles you can apply
them to any table to determine whether it is correctly normalized or requires further decomposition into two or more normalized tables. The examples will help you understand the principles as these use real world entities and attributes, if a little unrealistically.
You may be wondering why it is usually advised that people gain a good understanding of the first three normal forms rather than going beyond the third. This is partly because these are relatively easy to grasp, whereas with the higher normal forms the concepts
become a little trickier. However, it also reflects the fact that in most day to day situations normalization to 3NF means that a table is normalized to the higher normal forms (to 5NF at any rate). Unfortunately this is sometimes misunderstood as meaning
that normalization beyond 3NF is not important. This is certainly not the case, however, and where a business model demands normalization beyond 3NF, not to do so could lead to serious anomalies. Some time ago I recounted such a situation here, drawing on
my own experience in a Purchase and Supply department of a large manufacturing company, where not to normalize to 5NF would have allowed products which were sub-standard for certain uses to be unwittingly purchased. In this particular case the implications
were not critical, but if we'd been a car manufacturer and the products were components in the steering system of a vehicle, that would have been a different kettle of fish.