For Mail:
Restore
Make sure that Mail has run at least once so if this is a fresh installation run Mail and then quit it.
Open the directory Mail Settings on your backup
Open the directory [user] :: Library :: Preferences
Copy the file com.apple.mail.plist from the directory Mail Settings on your backup into the directory [user] :: Library :: Preferences on your computer.
Open the directory Mail on your computer.
Open the directory Mail on your backup.
Hold [CMD] and press [A] to select all the files in the backup directory.
Drag these into the Mail folder on the computer.
Answer "REPLACE" when asked.
Open the directory Mail Downloads on your computer.
Open the directory Mail Downloads on your backup.
Hold [CMD] and press [A] to select all the files in the backup directory.
Drag these into the Mail Downloads folder on your computer.
Answer "REPLACE" when asked.
DONE.
For Keychains:
Restore
Now restoration isn't just a matter of copying the file back or it would not be very secure would it !
We need to run a utility called
Keychain Access
Applications :: Utilities :: Keychain Access
Now once run you should see something like this
Now to restore our keychain we go to FILE :: Import Items
Navigate to the file stored on your external drive ([user] :: Library :: Keychains) and select it
You will now have to give the login password for the account at the time of the backup.
DONE.