2017 update: Now you can use @h-hellyer's solution (llnode, based on lldb rather than mdb). https://mcmap.net/q/530820/-tools-to-analyze-core-dump-from-node-js-closed
mdb + mdb_v8 is the way to go.
In order to use mdb, you will need a supported OS.
Now, most likely you will be running on Linux. If this is your case:
Part 1. get your core dump
You can get your core dump in many ways.
To get your core dump from a running process you can do this:
pgrep -lf node # get pids
gdb -p your_pid
# once in gdb..
gcore # this will output your core dump
detach # this will allow the process to continue to run.
Part 2. use mdb
There is a chance you know about Solaris, OpenSolaris, IllumOS or SmartOS. Most likely this is not the case. If you can afford the time of setting up SmartOS and mdb_v8, fine.
If not, install VirtualBox, and then autopsy. This handles the ritual of installing SmartOS as well as uploading your core dump files to the VM.
Once you are done, and when you are in your mdb session, you can then follow some of the steps from this presentation.