it depends on what exactly 'failed'. If the drive is still kicking you should be able to with no problems, just plug in the old drive and use the migration wizard.
The laptop was failed - could not power up and we did not have a similar or same laptop to put the drive in. We did have the drive in a USB external tray and we were able to "manually" transfer files. I would have like to have found a way to use Easy Transfer or something similar rather than the manual process. Still would like to know if there is an easier way.