How do I dive deep into code that does not have a single entry point?

Question

I work on enterprise Java projects that do not have a single entry point from where I can trace the flow of execution. Some of the projects have hundreds of classes, and when I'm asked to add a feature to a project, I often find myself at a loss as to where to start looking at code.

What's the best way to dive into such projects so that I can implement the feature quickly without wasting time.