Doc,
Here are the steps I followed.
1. Open Disk Utilities
2. In the left pane, click on the name of your external HD (Let's call it "EHD" from here on).
3. From the tabs at the top (e.g., First Aid, Partition, Erase, Restore, Unmount) select Restore
4. You will get a message: "Would you like to restore to "EHD"? The contents of the 'EHD' will be erased and replaced with the data from the volume selected below. Choose the volume you would like to restore to 'EHD'."
5. In the cell/menu below the message select your iMac HD.
6. Click on Restore.
That will initiate the transfer of data.
The term "restore" is misleading, as the data already exists. You will be simply copying it. In essence, you will transfer the data from your iMac to the external hard drive. Remember, any data existing on the EHD will be erased and replaced with your iMac data. To keep things simple on my transfer, I purchased a new external hard drive that was blank. Tip: Format the HD to Mac OS Externded Journaled, before transferring data. I have read that the typical formatting on new HDs are NTSB, a Windows format. Although I was able to transfer my data. I have heard that Time Machine only works on the Mac format.
Good luck...let us know if this works.