What the Internet is and is not:
There is no formal, structured "Internet". There is no Internet, Incorporated, or any regulatory body which exists to administer and/or otherwise control what goes on in the loosely joined world-wide network of computers which is commonly referred to as "the Internet".
The Internet is computer networking made easy. If you have the right software on your personal computer, you have the ability to log in to a large central computer, which will in turn will probably have the ability to log in to many other large central computers. And this is what "accessing the Internet" really means: finding the way through various computer networks into the resources that you need.
A good (and frequently abused) analogy for the Internet is a system of highways. But the highways do not link places like houses, cities, and parks --- they link computers. And while there is no "capital computer" on the map through which all highways pass, there are highways which have more traffic on them than others. These heavily trafficked pathways generally lead to the areas of most interest to the travelers. If you leave your house and you know the right turns to make, you will eventually wind up someplace that you are interested in.
Areas of interest could include anything. Absolutely anything. Federal databases, on-line keyword searches through library card catalogs, UPI and AP news wire services, National Weather Service updates, shareware, acoustic guitar discussion groups, Space Shuttle photography, and so on and so on. Given some time to explore, you too will find the places which you will want to visit the most often.
Who pays for the Internet? Everyone does. There's no centralized structure (although main groups do exist to address Internet issues: the Internet Architecture board, the Internet Engineering Task Force, and the Internet Society), so everyone pays for their own piece of the Internet. For example, the University of Tennessee pays for the UT computers which provide service. If you want to call that computer, you have to pay for your own computer and phone time.
This leads to an interesting ethic: when using the Internet it's best to use the avenues that are least expensive to whomever your host at the moment is. If you're combing the library of Congress on-line catalog from your PC in Knoxville, you do not want to use the University of California, Berkeley's computers to relay you to Sidney, Australia and from there into the Library of Congress. Use UT Knoxville's computer and go directly to the Library of Congress. This costs less in the long run and frees up national and international phone lines for those who need them more urgently.