I looked at this model before, but didn't suggest it as you were already out on your way to buy your cable. Anyways, I assume that the cables are grouped together side by side as opposed to a jumbled bundle.
If this is true, lay the cable flat on a table or floor. If the cables are aligned in the fashion shown on circuitcity's product photo, the green, blue, and red cables go for video. This red cable should be directly next to the blue. There will be a white cable next to a red cable. These two cables go into your speaker input.
From the picture there appears to be labelling around the color band of each cable. This might give you insight about which cable is what. The only confusion you should have is how to tell the two red cables apart, but one red should be on the outside of the bunch, and the other should be in the center (that is, if the cables all flatten out side by side).
EDIT: I hadn't looked at the monitor specs before, but I did so just now. On Amazon, it lists the inputs as 15pin D-sub, CVBS, S-Video and TV. It only lists "Analog RGB" because it mentions SCART. I assume that since your monitor doesn't have a SCART connection, it doesn't have analog RGB either.
If you do not have component input (R-G-B), then you most likely have at least S-Video. This should be a black connection with 4 female pin connections. There should also be a rectangular guide.
I'm not familiar with the xbox but I assume that you have to buy an adapter for S-Video output. That adapter should have the same stereo audio connections.
I'm sorry, but it looks like you're going to have to go back to the store. You're probably going to need something
like this. There are of course going to be other brands available as well.
I'm not sure how much better your performance is going to be on the LCD with this type of connection.