Try the command "netstat -an" from a command prompt. This should work for Windows, Linux/Unix, and Mac OS X. It will give you a list of all the network connections on your machine. Generally, you are only interested in connections where the state is ESTABLISHED. Also, connections with the local address of "127.0.0.1" are usually not interesting, as they indicate local-only connections.

For Windows, there is a much better tool for this that gives a more informative output with a GUI instead of a command line interface. Download TCPView, a free program. It will show an output similar to the netstat command, but it will also list the program name and PID (process ID) of which program "owns" each connection. Try the Show Unconnected Endpoints button to hide connections that are not in a state of ESTABLISHED. The Resolve Addresses command will perform a reverse-DNS lookup, which will display the hostname of the machines to which you are connected (if available), instead of their numeric IP addresses. TCPView even has an option to close a specific connection, if you right click on the desired row and choose Close Connection.

Using either netstat or TCPView, you can figure out which connections are inbound and which are outbound. Those with a Local Address ending in ":6881" through ":6999" (or any port number in the port range that you have specified) are inbound connections. The rest are probably outbound, especially if it has a Remote Address that ends in ":6881" through ":6999".

In the latest build of the experimental client (3.2.1b-2), if you click on the Advanced button you will get a screen showing details about each of the machines you are connected to for the current torrent.