Talk to maintainers. Approach them on email/twitter/project specific communities. Tell them you want to contribute and how you can be helpful. Most maintainers are looking for help. They will be happy to mentor you.
Thanks. Getting started is a hurdle - I often look at an interesting project on github and find it difficult to identify what can be improved.
Work on the non-sexy things first. Documentation, testing, promotion. These are the things that projects need the most to be successful.