Your editing software will probably first and foremost depend on the platform (or computer/operating system) you're using. Keep in mind, I'm not a regular user of any of these products -- as a professional I work in the much more expensive Final Cut Pro. However, if you're a user of one of the platforms below, these products are typically either already on your machine, or free to download depending on the software and platform. If you prefer a different editing software, or find a better tutorial, I hope you'll post your thoughts below.
Mac -- iMovie
iMovie comes preinstalled as part of the iLife suite on all new Macs. However, there have been significant changes in recent versions so if you have a Mac from before 2009, you may need to search for an older tutorial.
Here's the Vimeo Video School iMovie Tutorial
Windows -- Windows Movie Maker
I'm not as familiar with the version differences in Movie Maker, but I believe the below tutorial is specific to the version which comes with the base Windows 7 install (i.e. before the service packs). That doesn't mean it's useless if you've installed service packs, or you're on a previous windows version, just that you may want to keep an eye out for minor interface changes or tweaks. I don't think Movie Maker has experienced the same sort of complete overhaul that iMovie went through.
Here's the Vimeo Video School Windows Live Movie Maker Tutorial
Linux
If you're a Linux user there are a lot of video editing options, most of which are not designed to be simple or user friendly. From a simple, easy to use perspective, the most often recommended products appear to be OpenShot and PiTiVi. Let us know what works for you!