There are a lot of open source projects that are open to any help at all, as long as it conforms to at least a few best practice guidelines. For an example, take a look at jquery's policy: http://contribute.jquery.org/open-source/. They are very open and inviting for people to contribute.

I would suggest finding an open source tool or application you use often and finding their project (most likely on Github). Take a look at bug reports and issues. See if you can help out with these. Maybe they are just usage mistakes ("I can't get this thing to work right!!" "Oh, have you tried to click the button which does that? Here's a screenshot."). As you go through issues you'll find real bugs and some won't be terribly hard to fix. Jump in and fix it, then submit a pull request to have it merged into the project. The project will either accept the pull request or comment on it if they feel you a) need to add more to it or b) didn't actually solve the problem. You can then learn from their advice and soon you'll be far from a beginner.

Getting started in open source can seem daunting but really it's fun and not nearly as hard as it might seem.

Drupal is open to beginners too. See https://www.drupal.org/core-office-hours for more info. Basically, you can join an IRC channel and let them know you're new to the project and want to help, and you'll have a ton of people ready to assist.