I've researched a lot. (with the help of Google. :D) But would also love to get advices from people who have/had worked at an opensource project here. I would also love to hear your experiences.
If you've ever done any Node.js, there's an abundance of open-source modules out there that need to be tested, have features added and get bug fixes. Just pull one off GitHub and look through the readme for any noted issues/bugs.
If you haven't got any experience with Node, as AleMonteiro said, jQuery UI is a great project to get involved in.
How can I find a beginner-sociable mission? What attributes should I be searching for? What are advice signs that a mission might not be the right fit? Are there any tools out there to help session people with open source project?