If you're looking for a good video editing program, it's easy to become overwhelmed by all the options. Most good programs come at a price, but there are video editing options that come standard on most computers.
There are also some good programs that are web-based, meaning you don't need a program on your computer, but upload your clips to a ebsite and edit while you are online. Animoto is one such program, and is available for a low yearly price ($30 in 2009), but has the drawback of only allowing 10-second video clips. There is an additional cost to download high-quality versions of your movies, the cost is just $5 (as of 2009). You could also try the $3 trial for one video, which would also require a $5 DVD-quality download.
While professional-quality video editing systems like Apple's Final Cut Pro and Adobe's Premiere come with hefty price-tags, there are other video programs that you can buy for your computer at a lower cost. Muvee ($80, as of 2009) should have all the capabilities you need to make a simple video with music and narration.