If you can't restore from a Time Machine snapshot in Recovery, Setup Assistant, or Migration Assistant, then restore as much data as you can in the time-travel view.
Starting from a fresh installation of OS X, set up a new administrator account and log in. Enter Time Machine and press the key combination shift-command-C. The front window will show all mounted volumes. All snapshots should now be accessible.* Select the one you want and navigate to your home folder (in the Users folder at the top level of the old startup volume.)
You should now be able to restore your user data. I suggest you do this in two stages. Quit all applications except the Finder before you begin.
- Restore all the visible items at the top level of your home folder.
- Hold down the option key and select Go ▹ Library from the Finder menu bar. Enter Time Machine and restore all items in the Library folder. Log out and log back in as soon as the restore is complete.
Any other invisible folders or files at the top level of your home folder that you want to preserve will have to be restored separately. For most users, that isn't necessary.
Then either restore or reinstall all third-party applications, or restore them from another kind of backup, if you have one.
You'll have another problem if this is a new computer, or if you erased the startup volume: The next time you back up, Time Machine won't recognize any files as being the same as they were before, and will make a full copy of all files. There might not be enough space on one or more of your backup volumes for that. There are different ways of dealing with that situation, depending on your needs. The easiest way is to set your backup drives aside, if possible, until you're sure you'll no longer need the data on them, then erase them and start over. Meanwhile start a new backup on one or more empty storage devices. If that solution isn't workable for you, ask for instructions.
*If you don't see any snapshots in Time Machine, exit the time-travel view and then hold down the option key while selecting
Browse Other Backup Disks...
from the Time Machine menu, which has an icon that looks like a clock running backwards. Select the backups of your computer by its previous name. If you don't have the Time Machine menu, open the Time Machine preference pane in System Preferences and check the box marked
Show Time Machine in menu bar
