1. After you click the download link, you wait for Adium___.dmg to finish downloading.
2. You double-click the .dmg file that was downloaded to "mount" it. A dmg is a Disk iMaGe. When opened it shows up as if it were a virtual hard drive or CD.
3. Once mounted it shows up on your desktop as a white disk. Inside it, you will see the duck icon for Adium. In order to "install" the application, you simply drag the duck icon out of the dmg and into your Applications folder.