When I've been in this situation, I try one of three things:
Read all the code top to bottom. This lets you see what code is working, and you can report progress easily (I read through all the view code this week). This means you spend time on things that may not be helpful (unused code) but you get a taste of everything that is there. This is very boring.
Start at the beginning and go to the end. From the login page or splash screen, start looking at that code, then the next page, then the next page. Look at the view, controller, and database code. This takes some time, but it gives you the context for why you need that code or database table. And it allows you do see most often the ones that get used in the most places. This is more interesting.
Start fixing bugs. This has the benefit of showing progress on your new project (happy boss) taking work from other people (happy co-workers) and learning at the same time (happy developer). It provides the context of number 2, and you can skip rarely used code from number 1. This is the most interesting way for me.
Also, keep track of what you've learned. Get a cheap spiral-bound notebook and write down an outline of what you've learned. Imagine yourself giving a talk on the code you're learning about or bug you're fixing. Take enough notes to give that talk, and spice it up with a factoid or two to make it interesting. I give my notebooks dignity and purpose by calling them "Engineering Notebooks", put a title on the front (my name, company, date), and bringing them to every meeting. It looks very professional compared to the guys who don't show up with paper to take notes. For this, don't use a wiki. It can't be relied upon, and I spend a week playing with the wiki instead of learning.
As mentioned above, being the new guy is a good chance to do the things nobody ever got around to like unit tests, documenting processes, or automating running tests. Document the process to set up a new box and get all the software installed to be productive. Take an old box under someone's desk and put a continuous integration install on it, and have it email you when the tests fail. You can forward that email whenever someone else checks in code that breaks the tests. Start writing tests to figure out how things work together, esp. if there aren't any/very many tests.
Try to ask lots of questions in one-on-one situations. This shows you're engaged and learning, and it helps you find the experts in the different parts of the app. On a big project you may need to go to one person for one topic and a different person for other topics. It also helps identify who thinks they know more than they really do or who talks more than you really need.