Steps

1. Plug in a keyboard and monitor into your system

2. Power on, or reboot the the system (ctrl-alt-del on the keyboard)
   - You will get some form of bios screen - this example is from the NE-ONE Desktop hardware:
   
   

   Open

   

3. You now need to get the the grub menu, and as this has a short timer on it it can flash by. So right after you see the Bios screen above start "spamming" repeatedly pressing the left Shift key on your keyboard.
   You will now get the grub boot menu:

Open

1. Use the down arrow key to select "Advanced options for Ubuntu", then press the <enter> (return) key
   You get:
   
   

   
   
   

2. From here use the down arrow key to select the option Ubuntu with Linux a.b.c-dd-generic (recovery mode) [where the Linux kernel version: a.b.c-dd varies], then press the <enter> (return) key
   The system boots displaying various boot messages and then you get the recovery menu:
   
   

3. From here use the down arrow key to select the option root (Drop to root shell prompt), then press the <enter> (return) key.
   You get:
   
   

4. Press <Enter>
   You get:
   
   

   
   and you are now at the command prompt - logged in as root
   
   

5. To change the password of the user <username> enter the command:
   # passwd <password>
   and you are now prompted for the password:
   New password: ← enter the new password here
   Retype new password: ← enter the new password here (again)
   and provided that it worked you get:
   passwd: password updated successfully
   
   

6. Now you are back to the prompt (#) - press control-D to get back to the Recovery Menu and then choose resume (resume normal boot) from the menu to boot the system

7. Now press <Enter> (return) to exit recovery mode
   The system now boots. When complete you get the login prompt where you can log in as <username> with your new password