Most modems have between two and four plugs in the back. External modems have a power plug, and it connects to the power supply. Internal modems get their power from the computer's power supply. This connects the modem to the computer. If you purchased a new external modem, chances are you also need to buy a serial cable for this plug.
Internal modems connect to the computer through the system bus.
If you get these backward, it won't hurt the modem, but the modem won't work, either. In that case, the cable that comes from the wall should be plugged into it. PC-Card modems have a plug which goes into the computer, and a phone jack. Again, the cable which comes from the wall should be plugged into the jack. Back I have an external modem, and it has lights on the outside.