You need to boot from your backup disk using:
Boot Using OPTION key:
1. Restart the computer.
2. Immediately after the chime press and hold down the
"OPTION" key.
3. Release the key when the boot manager appears.
4. Select the desired disk icon from which you want to boot.
5. Click on the arrow button below the icon.
Once booted from the backup drive then:
Clone using Restore Option of Disk Utility
1. Open Disk Utility in the Utilities folder.
2. Select the destination volume from the left side list.
3. Click on the Restore tab in the DU main window.
4. Select the destination volume from the left side list and drag
it to the Destination entry field.
5. Select the source volume from the left side list and drag it to
the Source entry field.
6. Double-check you got it right, then click on the Restore button.
Destination means the now erased internal drive. Source means the external backup drive.
Once booted from the backup drive you need to partition and format the internal drive:
Drive Partition and Format
1. Open Disk Utility in your Utilities folder.
2. After DU loads select your internal hard drive (this is the entry with the mfgr.'s ID and size) from the left side list. Note the SMART status of the drive in DU's status area. If it does not say "Verified" then the drive is failing or has failed and will need replacing. SMART info will not be reported on external drives. Otherwise, click on the Partition tab in the DU main window.
3. Under the Volume Scheme heading set the number of partitions from the drop down menu to one. Click on the Options button, set the partition scheme to GUID then click on the OK button. Set the format type to Mac OS Extended (Journaled.) Click on the Apply button and wait until the process has completed.
4. Select the volume you just created (this is the sub-entry under the drive entry) from the left side list. Click on the Erase tab in the DU main window.
5. Set the format type to Mac OS Extended (Journaled.) Click on the Security button, check the button for Zero Data and click on OK to return to the Erase window.
6. Click on the Erase button. The format process can take up to several hours depending upon the drive size.
Steps 4-6 are optional but should be used on a drive that has never been formatted before, if the format type is not Mac OS Extended, if the partition scheme has been changed, or if a different operating system (not OS X) has been installed on the drive.