“What kind of modem do I need to connect my Xbox 360 to Xbox Live?”
The modem you will need to connect your Xbox 360 to Xbox Live is an external modem provided by your broadband ISP. Typically you will want to purchase a router to connect to the modem provided by your ISP, with your Xbox 360 connecting to the router. If you plan to use a wired connection to connect your Xbox 360 to the router, you need to connect the Ethernet port on the back of the Xbox 360 to one of the Ethernet ports on the router. If you want to connect your Xbox 360 using wireless, you will need a wireless router and the Xbox 360 Wireless Network Adapter.
Read more details about setting up a wireless network for your Xbox 360 or consider some of these Xbox 360 networking alternatives.
One thing I would not recommend is attempting to use Xbox Live over a dial-up connection. The connection will be far too slow for online game play. Even if you do manage to connect, you will have lag and make the other gamers in your online match unhappy with you.