For Replica Sets

Instructions for restoring a backup while changing the replica set name & members are as follows:

1) Restore the backup files into the new location
2) Bring up 'mongod' without the --replSet option: wait for recovery to complete
3) Shut down 'mongod'
4) At the filesystem level, completely remove the 'local' database. (If you're using 'directoryperdb', then just remove the 'local' directory)
5) Start up 'mongod' with the correct '--replSet' option
6) Perform a 'rs.initate()', followed by 'rs.add()' for each of the nodes you want to add to the set

For Standalones

The documentation covers how to perform a filesystem-level backup and restore using snapshots. However, it does not cover how to perform a filesystem backup using fsyncLock() and OS-level file copy, nor does it describe how to restore such a backup.