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 website and edit while you are online. Animoto is one such program, and is available for a low yearly price.
While professional-quality video editing systems like Apple's Final Cut Pro and Adobe's Premiere Pro come with hefty price-tags, there are other video programs that you can buy for your computer at a lower cost. Muvee should have all the capabilities you need to make a simple video with music and narration.
Here are two videos explaining the basics of editing in these free softwares:
In addition, there are plenty of Editing softwares to choose from. The industry most commonly used are Adobe Premiere Pro and Final Cut Pro, choose the one that fits your budget and will help you to creatively post-produce your content.
Here are a few other "Free" Video Editing platforms out there for you to use in a "trial basis" before you make your final decision on which one to purchase, again, according to your needs and budget.