You have a few different options depending on what version of 360 you have. If it's a newish version, then it will have a built-in Toslink optical connector. So, connect up an appropriate Toslink cable from Xbox to receiver and you're done. If you don't have a newer 360, then you can either purchase the HDMI audio dongle:http://www.monoprice.com/products/product.asp?c_id=108&cp_id=10830&cs_id=1083005&p_id=7526&seq=1&format=2
and use the Toslink method or you can use the plain old RCA analog L and R stereo plugs from the dongle.....or you could also do a Toslink cable from the TV to the receiver, assuming that your TV supports HDMI to Toslink for non-tuner sources. Some TVs do not support anything but 2 channel stereo over HDMI and so you'd still be limited to 2 ch stereo in that case. If you have an older TV with actual analog RCA audio outpus jacks, you can run those over to the receiver.
If you want 5.1 surround sound, you absolutely have to use one of the Toslink cable methods for your setup.
I should also mention that some folks have had trouble with the monoprice dongle not holding the Toslink connector tightly enough. It seems to depend on the Toslink cable. Some hold tight while others are loose enough to risk falling out. There are other sources for the HDMI audio dongle that may not have that issue. It's also possible that monoprice have addressed the issue in newer stock, but I have not heard that.