To take a screen shot in Mac OS X use the following key combinations:

Command+Shift+3 to do an entire screen capture
Command+Shift+4 to select an area of the screen to capture

Command is commonly known as the Apple key, and has the apple symbol and what people call the four-leafed clover on it.

Pictures should appear on the desktop as Picture 1.png, Picture 2.png, etc. (this is true for Mac OS X Tiger and Leopard, they could be a different file format in previous versions of the OS).

To record video there are a few commercially available screen capture programs (such as the excellent SnapX Pro), or a free program I know of which is good for 60 seconds of screen capture video is CaptureMe - available here:
http://www.chimoosoft.com/products/