If you check the back of your monitor for what connections it has, I can give you more information.
If you have the xbox elite bundle, you get a HDMI cable with it. If it's not then you'll just get component which is used to connect to older televisions.
If your monitor has a HDMI port on the back, its as simple as HDMI in to the 360, then in to the monitor. HDMI cables can be pricey ( I've seen them at £15) so shop around before buying
Otherwise, it'll have DVI (or if its an older/cheap model, VGA)
If its DVI, then you'll need a DVI-HDMI adapter
If its VGA, then I don't think you can use your monitor with the 360, I don't think it can handle the bandwidth throughput for it.