To get into Comms, you need three things: an Amiga, a modem and a telephone line. I'll assume you already have the first and the last, but the modem is often a source of confusion.
A modem (short for modulator-demodulator) is a device which takes the digital information (bits and bytes, a series of electrical pulses) which your Amiga sends out and transforms into an analogue form. If you pick up the phone when a modem is using the line, you'll hear a rather unpleasant screeching noise, which is the analogue signal being sent out by the modem.
This is sent down the telephone line and a modem at the other end takes this hideous noise and turns it back into digital form, which is then sent to another computer. This process works in both directions, so data can be sent and received by your Amiga. Because the information is digital, it could be anything from a PD program to a sound sample of a cow going Moo.
Many different types of modem are available, but the important thing to bear in mind is how fast the modem can transmit and receive data. In order to ensure that the different types of modem can talk to each other properly, several standards have been set up, which cover how the data is sent between the modems. These are the V standards. As the technology of modems has moved on, newer modems which can send data faster have been designed. To keep up with this, new standards appear every now and then. The latest (and fastest) standard is V.34 (also known as V-Fast).
Usually, the faster the modem the more expensive it is. However, a more expensive modem saves on phone bills, so it's a question of working out what sort of use you are likely to make of your modem before deciding whether to go for economy or speed.
For instance, you could probably pick up a cheap modem for as little as £40, but this would be very slow and would probably take around 25 minutes to download a 300K file, which would cost you approximately £1.25 if you were calling long distance.
A new V-Fast modem would cost you over £300, but it would download the same file in around 2 minutes, costing you about 15p in phone calls. As you can see, an expensive modem can save you a lot in phone bills if you regularly call long distance and download large files.