Transparent Encryption For a User's Home Folder
First install the package ecryptfs-utils:
sudo apt-get install ecryptfs-utils
Then load the ecryptfs kernel module:
sudo modprobe ecryptfs
And make it permanent in /etc/modules-load.d/modules.conf.
Assisted Encrypted Home Directory
The user whose home directory you want to encrypt MUST NOT be logged in. For example, you can be logged as root in a tty.
Then run as root:
ecryptfs-migrate-home -u <username>
When this is done the user must login BEFORE rebooting the computer.
If the user can access the files in the users home directory you can remove the backup folder in /home/<username>.<random characters>
The user should also run this command to get the random encryption key and store it in a secure location (outside the encrypted home directory and not on the same machine) in case a recovery is needed:
Assisted Encrypted Swap Partition
To encrypt the swap partition too:
sudo apt-get install cryptsetup sudo ecryptfs-setup-swap