What determines one's IP address? Is it his particular computer, his phone number, his address? And is it always the same at one computer, or phone number, or location?

Basically, your internet service provider has a list of IP addresses the 'belong' to it. If you look at all the addresses for a small to mid-sized service provider (such as a local provider, computers in an office on a common network, or computers on a college campus) the first few numbers will be the same for all of them. Larger providers (like AOL and MSN) have too many addresses for that, so they'll have different sets with different numbers.

Either way, the first few numbers describe your internet service provider so that things from the larger internet can be directed their and the rest tell your service provbider which of its costomers the data is directed to.

Broad-band "always on" connections (including cable, dsl, and ethernet) give each computer a fixed address. Dial-up networks sometimes do, sometimes don't. They may give you whatever number out of their pool of numbers isn't being used at the time you call.