Windows Movie Maker (free)
Windows Movie Maker is the Microsoft tool for editing video. Users of Windows prior to Windows 7 should look at tutorials for Movie Maker 2. Users of Windows 7 can use the tutorials for Windows Movie Maker Live.
Tutorials for Windows Movie Maker:
iMovie is Apple's consumer level video editing application. Apple has training material on their web site including some video tutorials.
Final Cut Pro (fee)
Final Cut Pro is Apple's video editing application geared towards professionals. Apple has some excellent training material on their web site including some video tutorials. UC Berkeley's Graduate School of Journalism has an online tutorial for Final Cut Pro.
Audacity is an open source audio editor for Windows, OS X or Linux.
Audacity can be downloaded from Sourceforge. For tutorials see the Audacity wiki.
GarageBand is Apple's consumer level audio editing application and is included free on all OS X Macs.
Apple has training material and video tutorials.
Acid / Acid Xpress (free/fee)
Sony's Acid Music Studio is a consumer level audio editor and is roughly equivalent to GarageBand except that it runs on Windows. You can down load a free trial version from the Sony web site.
Acid Xpress is a free version of Acid and has a smaller set of features than Acid.