Moving the current window to another desktop only with keyboard and mouse
Grab the window at the top so you can move it around the screen. Then move your cursor, while still holding and dragging the window, against the side towards the desktop you want to move it to. After a short pause the desktop will change a the window is now on another desktop.

In something more succinct: 


Grab the window in desktop 1 with cursor
Use cursor to drag the window over against the right side of the screen (so you can't move the cursor any further to the right)
After a short delay the desktop will change to Desktop 2
Release the window.