Usually you don't write a project and then sit down to read through all dependencies, but it's a process that happens when you do add a dependency.

So, the process would be something like: have a problem that a library might solve, find a library that could solve the problem, verify it can solve the problem, look through the implementation, look through it's dependencies, then actually include it in the build. If anything doesn't look nice at each step, rollback and find something else or start writing your own implementation.

Do this from beginning of the project and you'll always have a full understanding of the system.