While in Time Machine, 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 the files you want to restore.
If you need to restore from a backup of the hidden user Library folder, first select a snapshot, then press shift-command-G. A Go to Folder dialog will open. In it, you'll enter the path to the folder. The dialog will help you by automatically completing the parts of the path when you start to type them.
The path begins with slash character ("/"). Enter that. The rest of the parts will be separated by slashes.
The next part is the date and time of the current snapshot. Enter a "2", and the rest of the date should be filled in automatically. Press the right-arrow key to jump to the end of the path. Enter a slash to start the next part.
Next is the name of the volume (usually "Macintosh HD" unless you gave it a different name.) Start to type that, then jump to the end and enter a slash.
The next part is "Users", followed by a slash.
Next is your (short) user name, which is also the name of your home folder.
Finally, enter "Library", then press return. You should now be in the Library folder. From there you can get around as in the Finder.
