It should be a seamless install process right from the earthbrowser.com home page. However you do need to have Flash 9 installed in your web browser (and turn off any flash ad-blocking software). Even then some Mac powerbooks seem to have a problem.
The most certain method to install version 3 is to install adobe Air from http://get.adobe.com/air/ and then restart your computer.
Then return to http://www.earthbrowser.com and you should see the "install badge" in the upper right section of that page.
If you still do not see the badge, you should download the .air file directly from:
http://api.earthbrowser.com/version/latest/EarthBrowser.air/