Folder encryption
Encfs tool and automatic mounting with gnome-encfs.
Home folder encryption
During Ubuntu installation you can check Home encryption checkbox and fill the passphrase.
Whole disk encryption
The simpliest way is to use the Alternate Installer (special Ubuntu installation image, for example Ubuntu GNOME Remix) with LVM.
Password management in LVM
Typically your "virtual" LVM disc is on /dev/sda5.
List passwords
sudo cryptsetup luksDump /dev/sda5
Add new password
sudo cryptsetup luksAddKey /dev/sda5
You will be prompted to enter the old password first.
Remove old password
sudo cryptsetup luksRemoveKey /dev/sda5
You should have one more password to preserve encrypted disc accessibility.