I want to know how to separate an image from its background so that I can put it over another object.

The easiest way to do this is with Photoshop CS3 (not Illustrator). Photoshop CS3 has a Filter -> Extract tool that lets you outline the edges of the image and extract it from the background.

Here is a tutorial:

YouTube - Photoshop Tutorial :: Using the Extract Filter

The magic wand does a nice job in photoshop if it's a more or less solid colored background.