Here are my stories of getting involved in open source projects.
I was frustrated with the almost no doc of hamcrest-php matchers, each time I wanted to use a matcher I have to look through the code, some of my office colleagues were also frustrated, I initially wrote down some matchers example and later thought this would be a great fit to add it in the doc, I updated the README file, open a PR and it eventually got merged!
We use Phake mocking library heavily in our tests. In one case I found a method isn't working as expected in this issue, I opened a PR and added a comment in the issue. Even though I opened the PR back in March 2016, it actually got merged in March 2017!
This time add test coverage on PHP source! I attended a php conference in Atlanta, GA on May, 2017. Inspired by this talk, I opened a PR that added tiny test coverage, it got a vetting before getting merged!
Start with documentation, even if fixing a typo! Best way to start is look into your favorite framework/library/packages/whatever and see how you can contribute.
Check existing issues to see if there is anything that you can work on.
You don't need to be ninja/expert to contribute! There are places for everyone to contribute something/somehow that would help others.
Believe yourself and start contributing!