<p>When I downloaded Skype, I noticed that, in place of a normal "disk image" icon, there was a custom icon, and when I double clicked on the icon, the window used a colorful image as the background, prompting me to drag the skype icon into the applications folder.</p>

<p>How can I do that with my applications?</p>

<p>Thanks,
Jason</p>

Let me add to the other answers
jwz's howto
on setting view options on .dmg files. This is the simplest one that I got to work with no problems.
Also, to change the icon from the default .dmg icon:
In the Finder, open an inspector window (^I) for the file whose icon you want to use, click on the icon at the top (it will get a blue border) and copy it to the clipboard (^C).
Then open another inspector for your .dmg, click on the icon and press ^V to paste
(you can change the icon for any file like this).
For this kind of thing, you can always look at open-source programs and see what they do to get a similar result. For example here are the relevant source files for building pretty dmg files in:
Adium
Miro