If you need to change your root password but do not know the old one.
You will need to drop to a root shell. When you boot into your computer, as soon as the bios screen disapperes (the srceen with your computers logo on it), start tapping the Shift key untill the grub menu comes up, and if this option does not work, then tap the esc key. (if it is already configured to come up then this step is not nessessery)
When you see the menu choose the option of the latest kernel (or the one you normally use) and choose the option right below called "recovery mode"
It should look like this:

This will take you to a menu looking something like this:

Next choose the Root option
Wait and let everything load untill you get to a shell. Now comes the fun;
Enter the following command:
passwd "your username"
(no qoutes though)
If you are unsure of your username you can look at the names of the files in your home floder via:
cd /home
than enter
ls
This will show you the names of users on your computer.
Now type the command I stated above; passwd "your username" without the qoutes. So that if your username is jane, I would type:
passwd jane
Next you will be presented with an option to enter your new unix password. This is where you enter the password. It will ask you to retype the command and then after two successful passwords were entered the password has been changed. Now log back into your system via
reboot
If you are asked for your root password when entering your new password this will usually help:
Second Possible Step
"If you get asked for the root password when entering single user mode use 'init=/bin/bash' on the kernel append line which should boot the machine into a bash console where you can get read/write access to your /etc/shadow file. You can then either run passwd or edit the shadow file directly to put in an empty string. This allows you to reboot the machine into its normal environment and login as root leaving the password blank and then run the passwd program to set the root password. This should really only be done when the machine is detached from any networks." (taken from shawn lee in an article mentioned below)
If you need more information these links can help:
https://wiki.ubuntu.com/RecoveryMode
http://www.psychocats.net/ubuntu/resetpassword
http://www.debuntu.org/recover-root-password-single-user-mode-and-grub
http://www.debianadmin.com/how-to-reset-debian-root-password.html