I'd suggest starting with the tests. While Vue's test coverage is 100%, I'm sure there's room for improvement there. Reading through the test cases is also an excellent way to learn about Vue's internals and APIs.
Make sure to read the Contributing Guide, especially the section on project structure. It's also necessary to familiarize yourself with the development tools used (Flow, rollup, webpack, jasmine, karma...)
I also have plans for an in-depth guide on how to read and understand Vue's source code, but that will take some time to finish. :)