
1. Reset Your Ubuntu Password(in the GRUB)
Reboot your computer, and then as soon as you see the GRUB Loading screen, make sure to hit the ESC key so that you can get to the menu.
Root Shell - Easy Method
If you have the option, you can choose the "recovery mode" item on the menu, usually found right below your default kernel option.
Then choose "Drop to root shell prompt" from this menu.
This should give you a root shell prompt.
Alternate Root Shell Method
If you don't have the recovery mode option, this is the alternate way to manually edit the grub options to allow for a root shell.
First you'll want to make sure to choose the regular boot kernel that you use (typically just the default one), and then use the "e" key to choose to edit that boot option.

Now just hit the down arrow key over to the "kernel" option, and then use the "e" key to switch to edit mode for the kernel option.
You'll first be presented with a screen that looks very similar to this one:
You'll want to remove the "ro quiet splash" part with the backspace key, and then add this onto the end:
rw init=/bin/bash
Once you hit enter after adjusting the kernel line, you'll need to use the B key to choose to boot with that option.
At this point the system should boot up very quickly to a command prompt.
Changing the Actual Password
You can use the following command to reset your password:
passwd
For example my username being geek I used this command:
passwd geek
After changing your password, use the following commands to reboot your system. (The sync command makes sure to write out data to the disk before rebooting)
sync
reboot -f
I found that the -f parameter was necessary to get the reboot command to work for some reason. You could always hardware reset instead, but make sure to use the sync command first.
And now you should be able to login without any issues.
2. Resetting Ubuntu Password with LiveCD
You'll want to boot from your Ubuntu Live CD, choosing "Try Ubuntu without any change to your computer" from the boot menu.
Once the system boots, open up a new Terminal window from Applications>>Accessories and then type in the following command:
sudo fdisk -l
This command is used to tell what device name the hard drive is using, which in most cases should be /dev/sda1, but could be different on your system.

Now you'll need to create a directory to mount the hard drive on. Since we're actually booting off the live cd, the directory doesn't really get created anywhere.
sudo mkdir /media/sda1
The next command will mount the hard drive in the /media/sda1 folder.
sudo mount /dev/sda1 /media/sda1
Now it's time for the command that actually does the magic: chroot. This command is used to open up a shell with a different root directory than the current shell is using, and we'll pass in the folder where we mounted the hard drive.
sudo chroot /media/sda1
Now you should be able to use the passwd command to change your user account's password, and it will be applied to the hard drive since we are using chroot.
passwd geek
Note that you'll have to type your username after the passwd command in order to change the right password.

Now you should be able to reboot your system and log yourself in with your new password.