UPDATE: On recent versions of macOS (tested with High Sierra 10.13.4) you can restore from a networked drive directly from the "Restore from Time Machine Backup" option in the recovery mode. The following steps are not required (but are super awesome!).

Prerequisites:

– admin account & password
– AFP/SMB-share & server IP-address

1. Boot the Computer to Recovery Mode.
2. Open Terminal in the Utilities menu
3. At the prompt enter: cd /Volumes
4. Create a sub-directory in Volumes as a mount point for your time machine share:
   mkdir TimeMachine
5. Enter cd TimeMachine
6. Enter pwd. pwd should show /Volumes/TimeMachine

7. Mount the network share with your admin loginname & password:

   mount -t afp afp://adminname:password@ServerIPAddress/ShareName /Volumes/TimeMachine
   

   If your password contains wonky characters like :@\/ use URL encoding to protect them

8. Enter: ls -la. Note the exact name of your sparsebundle.
9. Enter: hdid /Volumes/TimeMachine/NameOfYourSparseBundle. You may enter the first letters of the sparsebundle name and then hit TAB. Hitting tab should auto-complete the Time Machine sparsebundle name. It may not look the same as above as it escapes spaces and special characters.
10. After auto-completing the name, hit return. If you return to the prompt the sparsebundle has been opened.

11. Enter exit and ⏎ and quit Terminal.
    Example steps 3-11:

    

12. Select Restore From Time Machine Backup and click Continue.

    

13. After a search it should show you the Time Machine Backups directory as a volume that contains your backup. Select that (in my example 'Time Machine Backups') and click Continue.

    

14. In the next screen you will see all the backups that you can restore from listed by time and date.

    

15. Select the backup you want to restore and continue and finally choose your destination disk:

    

If you only have one destination, you can use the tmutil command in the Terminal to replace it with a new one. If it's the same device as before just at a new URL, it will automatically figure it all out and re-use the existing backups.

If your remote share doesn't have a password on it, you can run:

sudo tmutil setdestination protocol://username@server-address/share-name

(where protocol is either smb or afp).

if it does have a password, you can use -p and it will prompt you for the password:

sudo tmutil setdestination -p protocol://username@server-address/share-name

Note that, unless you have configured passwordless sudo, the first prompt will be your local user password for sudo, and the second prompt will be the destination password for tmutil.

You can also use the -a flag to add a destination instead of replacing the existing one. See man tmutil for more info.

To configure a client to backup to a remote server, you use the tmutil command, and the setdestination verb.

tmutil setdestination afp://user[:pass]@169.254.x.x/share

This also assumes that you have share already existing as an AFP share on your TimeMachine server.

TimeMachine from client-side doesn't really care much about the remote server, except to mount the AFP volume.