The modem is a small box that connects your computer to the telephone jack. The modem can be placed inside your computer as well to keep things compact. Your computer will have to be able to handle the software provided by the company you chose. Anyway, you may want to phone the Internet access provider before making all your decisions on the computer you wish to buy. They will send you literature for free on their services.
Modems come in different speeds.
Most of the Internet access providers send you their software for free, so you don't need to worry about buying communications software. I have received copies of AOL and CompuServe for free when purchasing various pieces of hardware. She receives five free hours a month. Other companies charge more per month, but provide more fee time. The Internet access provider will if possible, give you a local number.