After asking lots of questions, I was pointed to http://make.wordpress.org/core/handbook/, which does a pretty decent job outlining the workflow. It helps to read a lot of tickets first to get a feel for what they're fixing - http://core.trac.wordpress.org/report/14 and then find a neglected (but fairly recent) but and chip away at it.
It's overwhelming, but I've found a great amount of confidence in just picking a (tiny) bug, fixing it, and watching the process work. Good luck to you!