The other thing is to look at some of the common compression techniques, notably zip and gzip, and learn their "signatures". Most of these formats are "self identifying" so when they start decompressing, they can do quick sanity checks that what they're working on is in a format they understand.
Barring encryption, an archive file format is basically some kind of indexing mechanism (a directory or sorts), and a way located those elements from within the archive via pointers in the index.
With the the ubiquitousness of the standard compression algorithms, it's mostly a matter of finding where those blocks start, and trying to hunt down the index, or table of contents.
Some will have the index all in one spot (like a file system does), others will simply precede each element within the archive with its identity information. But in the end somewhere, there is information about offsets from one block to another, there is information about data types (for example, if they're storing GIF files, GIF have a signature as well), etc.
Those are the patterns that you're trying to hunt down within the file.
It would be nice if somehow you can get your hand on two versions of data using the same format. For example, on a game, you might be able to get the initial version off the CD and a newer, patched version. These can really highlight the information you're looking for.