To find out the UUID of your partition just use the following command:
sudo vol_id -u
for example, if you want to find the UUID of /dev/sda6, using the command:
sudo vol_id -u /dev/sda6
The rest is then as in the past.
I found the solution here: http://ralph.n3rds.net/index.php?/archives/175-Adding-a-new-partition-in-fstab-with-UUID.html