I can think of two reasons to be looking at an existing app with which I have no previous involvement: I need to make a change or I want to understand one or more aspects because I'm considering using them as input to changes I'm considering making to another app. I include reading-for-education/enlightenment in that second case.
A real benefit of the MVC pattern in particular, and many web apps in general is that they are fairly easily split into request/response pairs, which can to some extent be comprehended in isolation. So you can start with a single interaction and grow your understanding out from that.
When needing to modify or extend existing code, I should have a good idea of what the first change will be - if not then I probably shouldn't be fooling with the code yet! In a Rails app, the change is most likely to involve view, model or a combination of both and I should be able to identify the relevant items fairly quickly. If there are tests, I check that they run, then attempt to write a test that exposes the missing functionality and away we go. If there are no tests then it's a bit trickier - I'm going to worry that I might inadvertently break something: I'd consider adding tests to give myself a more confidence, which will in turn start to build some understanding of the area under study. I should fairly quickly be able to get into a red-green-refactor loop, picking up speed as I learn my way around.