I want to know how to cut a cube and delete some parts of it!
Select the face where you want the window,
press E to extrude and move the newly created wall in the direction you want the extrusion.
You can delete then the selected face.
EDIT Another quick way to make a window is using the inset tool.
Select the face on which you want to make the window, press I and drag the mouse. That will create a new face of similar proportions connected to the edges of the original wall. Then extrude by pressing E and dragging the mouse to create the depth for the window.