The number one thing you can do is regularly use and exercise the piece of software of interest. Want to contribute to OpenSSL? Use it! Use it in a way beyond that of a "how-to" tutorial on a first Google hit.
Second, I would say start reading the manual, or at least skimming it. Get a better understanding of what the software actually intends to do, not what you think it intends to do. Remember that documentation is a part of software, so improvements are always welcome here!
Then, after, you can learn how to build the software. Make an easy modification (like changing a title, or changing something that gets printed out), and recompile and observe the change. From here you can look at a high level what gets built in what order, and what's important in the project.
Finally, you can start thinking about bugs that have been recorded in a bug tracker, or attempting to implement a neat improvement or feature. Look/ask for guidance, so you don't spend time doing something that ultimately no one will want or care about (which isn't to say it wasn't appreciated, but many projects have specific guidelines/goals/etc. and it's important your changes fit with those).