It depends on what kind of connections the monitor supports. Most support VGA and DVI, but getting support for either of those out of the 360 is going to require an intermediary device. If it supports S-Video, Composite, or even Component video inputs, that shouldn't be too difficult to do.
I don't know if the monitor has built in speakers or what, but it shouldn't be hard to route the audio cables to something else.
I just bought my son a 22" LCD monitor for his computer, under the impression that he could hook up his Xbox 360 to it. The monitor says its HD ready, whatever that means! I've been doing some research on this and I think I understand that this can be done using a VGA or DGI cable. Which one is preferable? The guys at Best Buy told me that the sound would be terrible. Is this true? When I read the reviews of the monitor (Viewsonic), people were saying that the xbox worked great with it. Can anyone help? Thanks!