1. Power down your equipment -- ALL THE WAY OFF
2. Connect the external drive with the bootable backup to your Mac.
3. Press the power-on button. Make sure the external drive is powered on.
4. As soon as you hear the startup sound, hold down the option key and KEEP HOLDING IT DOWN until the startup manager appears.
5. In startup manager, you should see at least 2 drives. Your internal will be there, AND you should also see the external drive (IF it's truly a "bootable backup").
Is it there?
6. Use the pointer (or the tab or arrow keys) to select the external bootable backup, then hit return.
7. Does it boot?
If so, be aware that when the desktop appears, it's going to look EXACTLY THE SAME as your internal drive, because after all, it's a "clone", right?
You can check which drive is the startup drive by going to the Apple menu and choosing "about this Mac".
8. Once you're booted from the cloned backup, and you're satisfied that you want to copy EVERYTHING ON IT -back to- the internal, I would suggest this:
a. Open Disk Utility and re-initialize the internal drive. You don't need to "zero-out" data, just do a quick initialization.
b. Launch CarbonCopyCloner.
c. Set up CCC with the external drive as your source and the internal drive as your target.
d. Let CCC do its thing. It may take a while to copy everything back if you have lots of stuff.
When done, power down, disconnect the backup, then power up without it.
Do you get a good boot from the internal?
Does everything look as it should?
If so, you're done!
