First make sure you have read & write access to the folder you're trying to restore to. You should be able to see its contents in the Finder, and to move files in and out of it.
This is an exception to the rule that you should never make any changes to backup data. I've tested this procedure in OS X 10.8 only. It should work with later versions, but I don't know whether it works in earlier versions. Use it only for files that were backed up from your home folder, or a folder on another volume created by you, and would normally be writable by you. Do not touch backups of system or application files.
In the Finder (not in the time-travel view), navigate to the backup volume, then to the folder named "Backups.backupdb", and then to the snapshot you want to restore from. The snapshots are folders labeled with the date when they were created. Inside each of those folders is a file hierarchy like the one on the volume that was backed up. Descend through the hierarchy until you come to a folder named "Users," and inside that, a folder with your user name. The procedure will be different if you're trying to restore files on another volume.
Select the folder and open the Info dialog (command-I). Click the padlock icon in the lower right corner of the window and authenticate. In the Sharing & Permissions section, give your account Read & Write access. You may have to close the dialog and repeat this step in order for the change to show up. Then click the gear icon and select
Apply to Enclosed Items
from the popup menu.
Try the restore operation again, in the time-travel interface.
