1. Go Pruning: Whether it's your movies or your music, we've all made some bad decisions along the way, so now's the time to get rid of it. Maybe it's a Katy Perry single you bought in a moment of weakness, or you still have your college roommate's DVD of "Dude, Where's My Car?" stashed in a drawer. If you don't plan on listening or viewing it again, dump it.
2. Buy Storage: If you're still hanging onto the physical media, you'll want shelves to keep your DVDs, BluRays or CDs clean and organized. You want something that will allow you to properly display your collection so you can access them easily. For digital media, buy an external hard drive to hold your movies and music, and then use an old CD spindle to hold all the discs you won't be needing anymore.
3. Go Digital: Both movies and music work well on your computer, and the only space you need is room on a hard drive or two. The popular favorite is iTunes, but there are plenty of other options too, so look around to see what you like. For movies, rip them using a program like Handbrake (or something similar), and CDs are just a drive and burn away.
4. Get Alphabetical: You could organize your movies or music by genre, type (HD vs SD) or any number of different options, but the easiest way to go is alphabetical. This way, you never have to wonder if you put something under "New Age" or "World Music," and can find your stuff easily.