Backup Data Failure

I just had the local Apple Store techs reformat my hard drive and reinstall OSX operating system 10.9.4.
Obviously, I needed to restore my files from an external disk. My efforts to do so ended in failure. The drive did appear in finder when it was turned on so I proceeded to disk utilities to restore my data.
All 3 attempts at doing so failed. Error code showed "restore failure, could not validate source." "error 254"
On one of the attempts, it stated something I don't recall know exactly but it has been consistent of late with the one described above. What to do. Any ideas out there?
Thanks
UPDATE! While browsing around a few minutes following this post, I came across an app that descrived itself as being the tool for the transfer of data, files, etc., from various sources. I was not aware of this when I wrote my note. I activated it to retrive my data from the back up drive and it seems to be doing so, with an estimated completion time of 2 hours and 15 minutes. Because of the lateness of the hour, I don't believe I'll see it's completion (hopefully) before the morn. I'll provide my findings shortly thereafter. Thanks again. I believe the app to be titled "migration assistant."

It is a new day and great morning for when I awoke, the "migration assistant" succeeded in retrieving all of my files. I'm back in business.

How did you take the backup in the first place?

I'd suggest that using Time Machine is the best method going forward.

But if you had a full disk backup then Migration Assistant is the way to go.

I don't believe it was a full system backup but, as you can tell from my posting, what do I really know? Lol. I assumed that my back-ups were data only excepting the system files. That was my guess. And, I was of the opinion that I had to go to utilities to affect the restore. I wasn't able too.
I started the "migration assistant" approach last night. It being 11:30 p.m. in the evening, I thought what's to be loss having it work overnight, especially when it stated that it would take some two hours and fifteen minutes to complete the migration.

When I awoke this morning, I went to the computer, awoke it to see that there was a notice from migration assistant that the system files on the backup drive were incompatible with the existing system files and that they were not imported. That sounded bad to me but, looking beyond that notice I seen my desk top as I originally configured it. I have been using it all morning without incident and everything has been restored, with the exception noted.

I have to believe that the program rejected the old system files because the tech's at Apple updated the system with the latest files. That's my guess lacking any other explanation.

For your information and all others that are interested, I don't think I used "time machine" per say. I'm not familiar with what implications that has. I used an external drive that I purchased from OWC for my back-up drive and in doing so, I had to choose it over the option "time machine." Maybe that's the reason I couldn't restore from disk utilities. I don't know and that might be info that you knowledgeable folks can use of future reference and that's why I mentioned it.

In closing, I have to admit, it's a great feeling to know that many of you here are available for consult and assistance. In this instant, Apple did there thing but, I'm sure that you guys would have been there to fill the void if they weren't. By the way, my two visits to Apple were cost free. Doesn't that say something for support?

Time Machine is just a piece of software built into OSX that uses any external disk (formatted for Mac) as a backup device. When the disk is connected Time Machine backups up your files (docs, pictures, music, application) but not system files. Once it's done a full backup the first time, it backs up incrementally. But it's just a set and forget thing, that's what makes it so convenient.

Should you need or want to do a fresh install or you get a new Mac and want to migrate your user data over you use Migration Assistant to read the Time Machine backup and restore your data.

If you used a third party tool to backup your drive that may well explain why there were system files in there that the migration assistant wont copy back for you to protect the integrity of the operating system.

Feel free to post here with queries any time.