You might be familiar with TechSmith's Camtasia, which some NUS staff use for screen recording. If you don't need such a powerful tool, you can consider Jing Project. It is a free tool from Camtasia, which is available for both Windows and Mac.
Jing is easy to use and let's you do annotated screenshots or short video captures of your desktop. Here's a short demonstration of how you can create a desktop recording using Jing Project. In this demo, I will demonstrate something simple - logging in to IVLE. Once you've installed and Jing is running...
Step 1 - Capture
Jing appears as a yellow ball docked on the side of your screen. I chose to let mine dock on the left. Mouse over the ball, and click Capture (the plus sign).

Step 2 - Choose area
Jing automatically selects the area your mouse is over. You can also select an area manually by clicking and dragging the crosshair.

Step 3 - Choose still or video capture
Click Image for a still screenshot. In this example, I've clicked Video. Recording begins 1 second after you click Video.

Step 4 - Record
Start doing what you want to show on screen. Talk as you are doing it. (You'll need a microphone for this.) You can click the Pause (||) button if you need to take a break. Cancel if you're not happy with the recording. It helps to plan and rehearse before hand!

Step 5 - Share or Save
Click Stop to finish the recording. You will be presented with a new window. You can preview the recording by clicking the Play button. If you're happy with it, you can Save it as a Flash (.swf) file or Share it. If you have not shared a video before, Jing will prompt you to set up a free ScreenCast account, where your video will be stored. From here, you can provide a link to the video or embed it in a website/blog. I have provided the link to the video as it is too wide to be embedded here.

View the end product | Check out Jing Project