Every couple of months I feel like I've learned so much more, it makes me think I need more experience before being able to contribute something worthwhile to any of the open source projects I use.
But if you want to do a lot quickly, you need to find a project in active development. If possible, get in contact with the developers and find out how they are coordinating and planning. Are they using email? Slack? irc? Hangouts? Meetings? Join in if you can!
Once you've decided to get involved, read the code and really understand it. Make sure you are meeting the standards and conventions the others are using, and that your additions are compatible with the rest of the system.
If your not familiar with git, you need to be: http://think-like-a-git.net
If you get a good idea, make something simple and open source it. Put it up on Github and maintain it, to show that you are capable and interested in contributing. This might help you with teams that are a little skittish.
And if for some reason you can't find a good project to join, then get a friend or two together and make one. You want to make something that is useful to people, and actually gets people interested.
Some items to you might want to pay attention to when getting your project off the ground are mentioned in the ChangeLog article they are discussing here: https://news.ycombinator.com/item?id=2162078