Know Your Meme has a simple guide on how to dispute YouTube when they take down one of your videos for allegedly infringing on copyright. This is a must-view/must-read for anyone who makes parody, commentary, or other content on YouTube that builds on existing content. Now, this is not about how to circumvent copyright laws -- it's about protecting your Fair Use rights when you've made something that is legal.
A critical resource linked to by Know Your Meme is the Code of Best Practices in Fair Use for Online Video. It's an extraordinarily detailed document about Fair Use and how it applies to online video specifically. If you don't have a few hours to read and digest that, just check out the Know Your Meme video below:
(If you have no idea why this is becoming a hot issue right now, check out this video about the "Downfall" videos and their recent removal requests by the film's production company.)