Formatting and recovery from backup.

I messed up my computer by installing Yosemite when it was not compatible with the MacBook I have. It ran fine but could not install everything else. Now I am trying to recover from my backup, but cannot as it tells me there isn't enough disk space. I now want format the drive and recover from the backup. I have tried everything, like reinstalling Maverick and trying to recover my backup, but failed as the backup is dimmed and inaccessible. This is the only way that I can see and recover from my backup, but the machine won't allow me to format the hard drive. how do I solve this problem. I only have 250 gig hard drive.