Is that the W2234S?
If it is then you have a 1680x1050 resolution monitor, with a 16:10 aspect ratio and the only video input is a VGA connection. Does, this sound correct?
If you plugged in the VGA connection from the 360 (you would need to buy the special AV cable) then it should work. However, the main issue is that the monitor is a 16:10 aspect ratio, but the 360 outputs in 16:9. Depending on how the scaling in the monitor works then you will either get a image that is slightly vertically stretched or with black bars at the top and bottom of the image.
As for sound, as the monitor does not have any speakers you will need to route the sound signal another way. Do you have PC speakers you would want to use, an AV amp or possibly just a set headphones? If you plan to use any of these (or another sound output) can you please give some detail, especially connectors?
May I ask, which version of the 360 console do you have? As this will dictate if you need to buy any new cables.