I've been trying to install the Xfce Desktop Environment more than once, with no success.
I typed:
sudo apt-get install xubuntu-desktop
and:
sudo apt-get install xfce4
(separately)
and then logged out and in again... but nothing changed, as I had no option to choose between two Desktop Environments.
What should I do?
You should see a small ubuntu logo next to your username on the log-in screen. When clicking it, a drop down menu should present you with the selection of all installed DEs. make your choice and enter your username/password after that.
Ubuntu 17.10
This is how it looks like on Ubuntu 17.10:
I had to reboot after installing XFCE, a simple logout was not enough.