Sytem.Net tracing
One of the easiest ways is to use the built in System.Net tracing. It is a matter of copiying a config file to your machine and re-running your application. Here is a very detailed article on how tracing works and how to enable it.

NetMon capture 
The other way is to sniff the network traffic using NetMon, Ethereal, or etc. Here is how you can do it with NetMon