Depends on what exactly you have for a cable modem. Is it a integrated modem/router (with multiple ethernet jacks out), or just a regular modem with a single ethernet jack for a single PC?
If you have the router, then all you have to do is run an ethernet cable from your router to the 360.
If you just have a modem, then you'll have to get some kind of router which lets you serve your internet access out to more than one device. The router can be wired only, or a wireless wifi kind (which also have wired jacks on them).
The 360 needs a wireless adapter to talk to a wifi router - wifi is not built in. The bad news is that 360 Wireless Adapter is about $100. The good news is that if you don't want to spring for one of those, I have one that was from my first-gen Xbox and they also work with the 360. You'd be very welcome to it. (Damon is actually using Ken's old Xbox one too and AFAIK it's working well.)
I would recommend networking the 360 with a physical cable if possible. You'll be avoiding any potential interferance/latency issues that can crop up.
If you can't, then be very careful when selecting your router. For whatever reason, Xbox Live is
very picky about your router hardware. Make sure that the router is Xbox Live and/or Windows Vista approved! (There'll be little badges/stickers on the packaging.)
The Xbox wireless adapters support 802.11B and G protocols, and you want to go for G. It does not support the new draft N ones, so don't worry about springing for one of those.
This Linksys one is currently on sale and is listed on
Xbox Live's list of approved routers. Let me know if you need help with hardware choices and/or installation.
Glad you're joining the 360 bunch!
