Install Weston, the reference Wayland compositor.
$ sudo apt-get install weston
From within X to launch Weston in a window, run;
If you want you can put a weston.ini file in your $XDG_CONFIG_HOME, check "man weston.ini" for the syntax or look it up on GitHub:
From Linux built-in kernel VT, press Ctrl+Alt+F1, and type:
To run Weston on Wayland, not under X.
If you want to run legacy X11 applications on Wayland, you need to install XWayland.
$ sudo apt-get install xwayland
You can configure Weston to use XWayland by loading xwayland.so in your "core" section of your weston.ini config file. See "man weston.ini".
GNOME on Wayland
$ sudo apt-get install gnome-session-wayland
Now to run GNOME with the Wayland session, either install GDM (sudo apt-get install gdm), which is the GNOME Display Manager to replace LightDM, then you can select "GNOME with Wayland" as your login session.
Or Ctrl+Alt+F1 and run (I think it was this if my memory serves me right);
$ gnome-session --session=gnome-wayland