You'll figure out an approach that works for you, and you will hone your skill. Here are some pointers to help you get started.
Throughout the process, keep updating your mental model of how the application works. (You can draw components if that helps.) If you don't know what does something, then you can just make it a black box. Eventually, you can replace the black box with the actual component. For example, you know there is a “compiler” black box for Java. You don't need to know what the details are for how it works, but as you learn more in CSCI210, you'll understand what the compiler is actually doing.
Start from the high-level and work to the low-level.
Start at the beginning and trace through the application. For example, start at the home page of the web application. What code created that page? Click a link or button to go to another page. How did you get there? What code was involved in that process?
You can use a debugger and put breakpoints in the code to follow the code.
What is the “vocabulary” of the project? What are the nouns that describe the data and the verbs that describe the functionality? What keywords should you use to search the code base for how this works?
Try to make some small changes to the code and see how they affect the application.