Move the map around: drag with the mouse / arrow keys.
Zoom in/out: mouse wheel / '+' and '-' buttons (doesn't work in full screen) / buttons under the minimap.
Hide menus: TAB
Full screen: F11 / button in the top menu
You can move troops by dragging them with a mouse.
You can hide the toolbars by clicking the small arrows in the middle.
You can minimize game menus and drag them around to another position.
Click on a city twice for the unit movement menu.
Transporting units: open the Move troops menu, select units and click on the 'Load' button (this requires Air or Sea Transport on the same spot). Outside the cities, if there are enough transports for all land units, you can simply drag and drop the army.