Davinci Resolve is an incredibly powerful editing program developed by Blackmagic Design. They offer it for free to anyone, with the option of buying an upgrade that unlocks certain functions. For the most part those functions, while totally amazing, aren't necessary to the vast majority of everyday video/audio/color tasks. So what they have here is a software that rivals Premiere, Avid and Final Cut Pro X that is 100% free to use!
You can find a guide for installing it here
Below is an beginner's tutorial for Resolve that discusses the interface, loading your clips, and important editing tools.
Basic Motion Graphics in Resolve
Adding Titles in Resolve
Audio Editing Guide