Does the project have a suite of well-maintained unit tests? The unit tests are programmatic documentation for what the code does.
In addition, you need to learn enough about the architecture of the application to identify the places where you need to insert code for your new features, and more or less ignore the rest. You don't need to know the whole code base to do this; if the projects are well-architected, the functionality is already sufficiently encapsulated and decoupled that you can focus on the relevant parts. If you're lucky, the projects already follow a well-known architecture which will serve as a map for you to follow.
Code always has one or more entry points. For MVC projects, the entry point is a controller method based on an URL; the method will almost certainly access a data repository, and return a view. Start there.