You want to make a screencast. There is a lot of software out there for both the Windows and Mac OS X platforms.
If you just google for "screencast software" you'll have hours of reading ahead of you. In particular, the Wikipedia page, Comparison of Screencasting Software would be a perfect place to start. They list over 30 screencasting applications, telling you where to download (or purchase) them, which platforms they run on, and if they are commercial or proprietary, or open source or not.
The second charts tells you, for each of the 30+ apps, if they can record audio, record the entire desktop, supports OpenGL or DirectX, and if the app supports editing.
The link at Indoition helps you select a screencasting tool based on features, including: