Chrome has a built-in debugging tool for WebRTC, which can be found by browsing to chrome://webrtc-internals.
You can also view log output for Chrome by providing some command-line arguments:
~$ chrome --enable-logging --vmodule=*/webrtc/*=1
More information on logging in Chrome in general can be found here, and WebRTC-specific logging information can be found here.
Firefox has a built-in debugging tool, which can be found by entering about:webrtc into your url bar.
Additionally, a plugin can be installed to provide extra features, more info can be found in the Mozilla blog.
Logging can be enabled via the about:networking#logging config page. Logging must be enabled specifically for each module you wish to debug. Information on which modules you need to enable can be found on the Mozilla wiki.