The latest stable version of Audacity for OS X can be downloaded from http://audacity.sourceforge.net/download/mac.
Click on the link labeled "Audacity 2.x.x" to begin downloading.
Once the download is complete, you should see something like this on your desktop or in the folder that your web browser is set to download into:
Double click on it to begin installing the software.
You should now see a finder window with a disk image named "Audacity 2.x.x"
All you need to do now to complete the installation is copy the disk image into your "Applications" folder. To do this, click on the disk image to select it then press the Apple and C keys together to copy it. Now select your Applications folder and press the Apple and V keys together. This will paste an Audacity folder containing all of the contents of the disk image into your applications folder.
The installation is now complete, so you can eject the installer folder (by dragging it to the eject icon) and start using Audacity.
To open Audacity double click on the following icon in the Audacity folder:
The first time you launch Audacity you will be prompted to select which language you want it to use.
Click on the dropdown menu to select the language you want.
Once you have chosen the language you want click on OK to finish launching Audacity.
You should be able to see the Audacity interface which looks like this:
That's it! You now have Audacity up and running and can begin making and editing recordings.