The modem is wired to the Internet via the cable company's coaxial cable, the telephone company's DSL phone line, Verizon's FiOS network or a satellite modem. The router is wired to the modem.
Most ISPs charge between $10 and $15 monthly for equipment -- you should be able to see the fee on your ISP's broadband ...
We have it on good authority that Verizon will be discounting a handful of handsets and a few broadband access modems, possibly as soon as January 22nd. This would be an unusual out of cycle ...