Go to System -> Administration -> Synaptic Package Manager
Use the Search function and search for compizconfig-settings-manager, click on it and select Mark for Installation
Again Use the Search function and search for emerald and gnome-compiz-manager, click on them and select Mark for Installation
Finally click on Apply
To access Compiz Fusion, Right click on Desktop -> Change Desktop Background -> Visual Effects -> Custom -> Preferences
Keyboard Shortcuts
Here's a list of the most common Compiz Fusion keyboard shortcuts:
SUPER+SHIFT+DRAG LEFT MOUSE = draw fire
SUPER+SHIFT+C = clear fire
CTRL+ALT+DRAG LEFT MOUSE = rotate cube
CTRL+ALT+LEFT ARROW = rotate cube
CTRL+ALT+DOWN ARROW = flat desktop
SHIFT+ALT+UP = initiate window picker
CTRL+ALT+DOWN = unfold cube
ALT+TAB = window switch
SUPER+TAB = flip switcher or ring switcher, depending on which is enabled.
ALT+F7 = initiate 'move windows'
SHIFT+F9 = water effect
SHIFT+F10 = slow animations
CTRL+ALT+D = show desktop
For Grouping and Tabbing:
SUPER+S = select single window
SUPER+T = tab group
SUPER+Left = change left tab
SUPER+Right = change right tab
SUPER+G = group windows
SUPER+U = ungroup windows
SUPER+R = remove group window
SUPER+C = close group
SUPER+X = ignore group
Hold the SUPER button then select the windows you want to group and then hit SUPER+G.
The SUPER key is the Windows key on most keyboards.
Special thanks to FalkoTimme