Installed new SSD. How do I get my files back from Time Machine?

Question

Hi all, if you take the time to read my issue, thanks a lot. I appreciate any help you can offer, and sorry if anything is unclear...
The 1tb drive eventually failed on my 2009 27", quad core i7 imac. I had USB backup using time machine to an external 2 tb disk.
Repair guy took my mac to his shop, and installed a new samsung 1tb SSD.
He had trouble reinstalling from my time machine backup - so he's just installing Yosemite (I was using 10.8.x?) and giving it back to me with a fresh install of Yosemite.
When he tried to use time machine to restore my system to how it was, he started the process, and it said that it would take 13 hours, so he left it overnight.
When he returned, he found a white screen with a frozen mouse pointer. He did a hard reboot, and then could not access the drive at all - the system would not allow him to read the drive and he had to take the drive out, reformat from another mac, and then install Yosemite again.
Now he has suggested that I simply drag and drop all my folders from the USB time machine backup into my computer, and seems to think this will get things back to how they were. I'm not sure that it works like that though...I'd expect certain applications need to be installed, settings changed, permissions granted, passwords entered...that kind of thing.
Now I have a choice - whether to
A) reinstall my applications one at a time, and then copy the data from my backup drive.
B) manually drag and drop all the files from the most recent backup folder into the "computer" folder. (This was his suggestion)
C) attempt some kind of migration using the Migration assistant.  (I believe this is what the guy tried- he started it off, it said "13 hours remaining) he left it running overnight, and came back to a static white screen with frozen mouse, he powered down, then when he switched it back on, the screen did not load any OS (not sure whether it had booted into some kind of BIOS, but he said it was so unresponsive that he had to remove the drive and reformat it from another computer).
D) Try some other application for intelligently restoring my apps and data from the Time Machine backup.
To be honest, my main concern is screwing things up badly! I'm veering towards reinstalling my apps, even if it means fixing up preference settings and typing in codes etc... I would rather take a slow and steady approach rather than a "risk having to take it back to the shop/take it apart" approach.
Also, is migration different from restoring from time-machine?
Perhaps you could advise me? Many thanks

Answer 1

Restart the computer and hold the Command & R keys.
Thanks - I didn't know how to do that!
I did that, and it went through the steps for restoring from the time machine backup. I didn't click on "restore" just yet... My concern is that when the guy in the shop tried that, it resulted in the serious failure that required the drive to be removed and formatted from another computer.
I'm wondering what might have caused that - is it possible that the external drive had a failure, or (more likely) that the drive caddy it sits in briefly lost power or something?
Also, can you tell me if simply drag-dropping the files from the time-machine backup would result in everything returning to its initial state? Or is that (as I suspect) a bad idea?
Right now I have a fresh Yosemite install which works. I'd rather have that, and slowly restore my files and apps manually than risk getting the same result as the guy in the shop. Do you think that restoring from the restore partition is worth trying again?