Note that there are different versions of Audacity for different types of Mac—PowerPC or Intel with OS X, or OS 9. You must select the version which is appropriate for your Mac.

Downloading Audacity will create either a folder, which you should copy to your Applications directory, or a .dmg file. If you have a .dmg file, then double-click it. After extraction, you will have an Audacity folder, which you should copy to your Applications directory.

Unzip LAME MP3 if necessary, and copy the unzipped folder to the Audacity folder.

Next run the Audacity installer you downloaded.  

Then unzip LAME MP3, and copy the unzipped folder to the Audacity folder, which is in the Program Files folder.