Note: This applies to ClipMate 6&7, and assumes that you've made a backup using the internal backup routine.
Option 1 - Simple Restore: With ClipMate running, use File | Restore Database (needs v6.2 or later) to overwrite the current database with the contents of the ZIP file. Note: this will
overwrite any new data made since the backup.
Option 2 - Preserving existing data. Let's say that you have an old
backup that you want to restore, but don't want to overwrite your
existing (new) database.
So make a new database (see Config | User Preferences | Database) and call is "lifeboat". Make sure that you give it a new directory, other than where the primary one is stored.
Re-start ClipMate, and use ClipMate Explorer to verify that you see both databases in the collection tree. You should have your original database, plus the new one. The new one will contain empty default collections of Inbox, Safe, Trash, and Search. There may be a "welcome to ClipMate 6" clip in the InBox. Make sure that the InBox of the LIFEBOAT database is active. Then use File | Restore Database, to restore your ZIP backup into the LIFEBOAT database.
You can then move important clips from one database to another, and then you can
de-activate (with that same User Preferences dialog) the database that
you don't need anymore (probably the "lifeboat").
Note that in this example, we wanted to keep the new database, and use the old one temporarily, so we called it "lifeboat". You could go the other way, and use the new database as your "keeper". So give it a better name, like "New Database" or "My Clips2004".