Node.js: How to attach to a running process and to debug the server with a console?

From http://nodejs.org/api/debugger.html:

Advanced Usage

The V8 debugger can be enabled and accessed either by starting Node with the –debug command-line flag or by signaling an
existing Node process with SIGUSR1.

Find the PID of your node process and then sending SIGUSR1 should do the trick:

kill -s SIGUSR1 nodejs-pid

Then run node-inspector and browse to the URL it indicates. More in this tutorial.