If your monitor has a high definition connection, or HD connection, you shouldn't have to run through your tuner card, as it'd be as simple as plugging the XBOX 360 straight into the screen via the HD cable which should come with it since the xbox 360 is HD ready.
What you'll need to do then is check for this. If not, you might be able to get a HD to VGA convertor to connect the HD cable to the xbox, and straight throguh to your monitor, which might be possible.
If not, you can just go through the tuner card, though quality won't be as good as most only hav RCA cables (red, white, yellow) sockets, and so colour bleeding will occur on the images
I hope this helps