First, I'll give you the official answer:

Xbox Live does not support dialup (56Kbps and lower) modems that operate over ordinary analog telephone lines.

The connection in the back of your Xbox is not a telephone (RJ-11) jack, it is an ethernet port that uses an RJ-45 jack (it's much wider, although an RJ-11 jack *will* fit there, giving you the impression that perhaps that's where it should go... but it won't do you any good.

The Xbox is only designed to be connected, via an ethernet patch cable (I think the Xbox LIve starter kit comes with one) to the ethernet port on a cable modem or ADSL router, connected to high speed Internet either over a cable television cable (75 ohm) or a digital telephone line that supports some flavor of *DSL technology (RJ 11 again).

That's the end of the official answer.

The unofficial answer is that if don't have and can't get some kind of high speed access, it can still be possible to connect your Xbox to the Internet for use with Xbox Live using your dialup connection, if you're willing to spend a little bit of cash.

Some wireless routers-- most notably various editions of Apple's Airport, have plugs for ethernet ports but ALSO RJ-11 ports for connection to a phone line. You can use Apple's software (you WILL need a Mac for this, unless you want to play around with several of the cross-platform, java-based router configuration programs, which can be a little temperamental) to input your username, password, and phone number for your internet provider.

Then you can use an ethernet cable to plug in your Xbox to the Airport. (If it's one of the newer models, it has two ethernet ports, one for WAN (wide area network, for a high speed connection to an ISP via cable modem or ADSL router) and one for LAN (local area network, for hooking up one or more computers or other devices in your home). Plug the Xbox into the LAN port. If your wireless router is another model, or an older airport, it's only got one ethernet port, so you'll need a couple of more cables and a hub to hook everything up all at once.

The upshot of this is that, while the airport is connected to the Internet via your ISP, the Xbox can also share that connection to get Xbox Live working. If you do this via a wireless router like airport, it's also possible, through devices like Linksys' WET11, to connect your Xbox to your new "home" network wirelessly, without the ethernet cable. This is convenient if the Xbox and the TV are not in an area where it is convenient to string cable over to wherever your phone line and computer are. (I have one of these and use it, it's nice. In fact, this whole scheme is exactly what I use to connect to Xbox Live).

However, some warnings: setting this up does require some knowledge of network configuration, will require probably a couple hundred dollars in equipment and cables, and will give you an Xbox connected up to a service that assumes high speed access over a low speed line (I play Mechassault this way, and the lag is absolutely awful).

Hope that answers your question.