1) What kind of radio is used and what radio channels are used
2) Whether the operator chooses to communicate in "Real Time" (similar to a chat room) or by "Packet Mail".
Let's elaborate:
Some radios are intended to operate on the "Shortwave Radio Bands". These radios are capable of allowing the operator to communicate world-wide. If you've ever had a shortwave radio and listened to the BBC, you can understand that Ham radio operators have a similar capability.
However, there are also radios that Amateurs use for more local communications, like two-way radios that Police and Fire departments use. This is the most common way that Amateurs use Packet Radio. They rely on a network to "relay" their communications to more distant areas, sometimes utilizing the services of shortwave packet radio stations, or the Internet to complete "long-haul" communications.
Amateur packet radio also has a number of operational modes. Operators can contact each other and have a keyboard-to-keyboard chat in real time. They can also send mail to each other, similar to E-Mail that most people are familiar with. Using amateur packet radio for mail also relies on a network of Bulletin Board Systems (BBSs) to relay that mail to the intended destination. Very many locations world-wide are accesable via packet radio mail.
The Internet is well-funded, has a lot of people hired to expand it's network and is commercially supported. Amateurs are a much smaller, and more independent group of people.
If you already a ham, here's a good place to look for good basic information: The Tuscon Amateur Packet Radio Association. In addition, you can consult the "Packet Primer" section on this site.
Once you learn a little more, your best bet is to look for a local ham to help you out. He or she will know about local operating frequencies and conventions.
You'll need a Terminal Node Controller. New, most cost in the range of $100-$200 U.S. There are cheaper alternatives, however. Used units are fairly cheap, and a local ham radio operator who dabbles in packet radio may well know of a cheaper unit to buy, or perhaps one you can borrow to see if you like packet radio. Some operators are even able to use the sound card in their computer instead of a TNC.
You will also need a computer, of course. And it does not need to be one with great capabilities. There are many people who use an older computer dedicated to packet radio, such as an old 8088, 286, 386 or 486 based computer. Of course you can use your "family P.C." or MacIntosh computer to try out packet. You don't need a dedicated computer. Some Hams just find that to be a more convenient arrangement.
The computer must have a free serial communications port, and you'll need a serial cable to connect the TNC to the computer. There's another cable you will need to connect the TNC to the radio. Preassembled cables are available for the more popular TNC and radio combinations. Most hams elect to fabricate one themselves with parts obtained from a local electronics store, like Radio Shack.
There is a wide range of software available for use on packet radio. It ranges from software that you may already have, such as a standard "terminal program" like Windows "Terminal", "Hyperterminal" or "Procomm" (DOS or Windows versions) to complex programs designed to run on a dedicated computer. The good news is that software cost is seldom an issue as you may already have it, or can get "freeware" software written specially for the purpose. It is not necessary to run Windows to use packet, Apple and DOS users aren't discriminated against.