There are many important rules in the Code, not just a few, covering all sorts of aspects of nomenclature it might be better to ask about particular topics that people want to know about.
The main objective of the Code is STABILITY, names should only change when they actually have to in order to comply with articles in the Code. To this aim many new clauses were added in 1999 to help preserve prevailing usage of names that otherwise may have to be changed.
One important point that should always be born in mind is the difference between nomenclature and taxonomy. Nomenclature is governed by the rules of the Code, and only involves the way animals are named and the structures (eg. types) that are in place to fix names. Taxonomy uses the Code and the available names to convey relationships between taxa. For instance whether a taxon is a species or a subspecies is a taxonomic decision, and is NOT covered by the ICZN Code. The Code is used by taxonomists to decide what are the correct names for the animals they are studying, eg if a taxonomist decides that 2 taxa are actually the same species they use the Principle of Priority in the Code to choose the oldest available name as the valid name of the species as a whole. Other articles in the Code help a taxonomist decide whether a name is available or not - such as whether it is validly published, a junior homonym or an infrasubspecific name. It is important to bear in mind that the Code does not regulate taxonomy, only the nomenclature that taxonomists use.
Of course compliance with the Code is really voluntary, but the taxonomic community as a whole complies with it because it makes sense to have a single set of rules that everyone follows, so that there are not completely different classifications because some taxonomists follow one set of rules and others another one. The one major exception to this is that Lepidopterists generally (except the Japanese) ignore gender agreement rules in favour of original (or prevailing) spellings. The general opinion of Lepidopterists is that gender agreement is an anchronism and not science. However, this only affects the ending of some species or subspecies names rather than the whole name, so does not create much confusion.
There are actually two main versions of the Code, one English and one French. Both have equal weight, and sometimes one version can be used to clarify ambiguity in the other language. There are also translations of the Code into several other languages, but those do not have authority over the English and French versions.
The English version is online here:
iczn.org/iczn/index.jspAnd the other versions can be found here:
iczn.org/other_languagesThe Code is organised into various Chapters to make it easier to find relevant articles (= rules). Here is an overview (A = Article):
Introduction (aims of the Code and changes from previous versions)
Chapter 1 A1-3 Zoological nomenclature
Chapter 2 A4-6 The number of words in the scientific names of animals
Chapter 3 A7-9 Criteria of publication
Chapter 4 A10-20 Criteria of availability
Chapter 5 A21-22 Date of publication
Chapter 6 A23-24 Validity of names and nomenclatural acts
Chapter 7 A25-34 Formation and treatment of names
Chapter 8 A35-41 Family-group nominal taxa and their names
Chapter 9 A42-44 Genus-group nominal taxa and their names
Chapter 10 A45-49 Species-group nominotypical taxa and their names
Chapter 11 A50-51 Authorship
Chapter 12 A52-60 Homonymy
Chapter 13 A61 The type concept in nomenclature
Chapter 14 A62-65 Types in the family group
Chapter 15 A66-70 Types in the genus group
Chapter 16 A71-76 Types in the species group
Chapter 17 A77-84 The International Commission on Zoological Nomenclature
Chapter 18 A85-90 Regulations governing this code
End Pages (including the Glossary which contains definitions of the terms used, an important part of the Code for interpretation of meaning of words in the articles)
I hope this helps give a general overview. Perhaps people can ask about specific points they would like explained in more detail.
Adam.