I'm probably repeating myself, but I hope not frequently enough to annoy anyone:

You can check the Pull Request Club. If you join, you'll be assigned one project a month to contribute to. For me, it was a magnificent way to learn about existing modules, understanding their source code, different styles and restrictions they follow; to get in touch with their authors and maintainers, to get familiar with testing, development and deployment tools. I even got a T-shirt! :-)