here is another procedure. I assume you used the alternate installer and used lvm to create an encrypted root and swap partition.
1.) Boot from the liveCD and become root by typing into a terminal
2.) Install some tools (You will need internet access for this to work)
aptitude install cryptsetup lvm2
3.) Assuming that /dev/sda7 is the partition that holds your encrypted filesystem
cryptsetup luksOpen /dev/sda7 sda7_crypt
You should be asked for your passphrase now. Enter it. If everything went well it should display something like
Key slot 0 unlocked.
4.) Make your logical volumes visible
The result should be something like
2 logical volume(s) in volume group "ubuntu" now active
Enter the following
It should list the names of the logical volumes. One of them should be named root or so.
5.) Mount the logical volume named root.
mount /dev/ubuntu/root /mnt
If everything went Ok, then you should be able to access your files in /mnt. After you have copied your files to a secure location (thumbdrive, external harddisk... just not to the temporary filesystem of the liveuser) you can unmount everything and close the encrypted drive.
vgchange -a n
cryptsetup luksClose sda7_crypt
That should be it. If your setup varies or if any of the command fails post exactly what you have typed with the corresponding output up to the command that failed.
Hope this helps.