Here's how I did it:

• Download and unpack the Linux version.
• From the Finder, double-click the gmail-backup.sh file. You should get a prompt about whether you want to open an application from the dangerous internet ;), confirm that you do. It won't work but this step should mark the file as OK to execute.
• Now open Terminal.app (it's in Applications/Utilities).
• Now you need to make a directory to hold your backup data. You can make it however you want, but I just entered the following in Terminal:
  cd ~/Documents
mkdir GmailBackup

• Now, from the Documents directory, run this command by entering it into the Terminal window:
  ./gmail-backup.sh backup ~/Documents/GmailBackup/ your-gmail@gmail.com your-password
  where your-gmail should be replaced with your gmail user name and your-password should be your Google account password.