I don't think the 360 can browse the web. At least not officially, modders might be able to. Xbox Live is a contained service and does not allow surfing of the actual internet. You only have access to downloads, demos and games and patches that are in the Xbox Live service but nothing more.

Be cool if it did. I spent 4 years browsing the web with my Sega Dreamcast (seganet dialup, then earthlink when seganet went down) as I didn't own a PC until 3 years ago.