How can I pump water from our 2nd floor down to 1st floor drainage?
You can find a manual siphon pump at any large hardware or automotive store. It will look like a hand-sized rubber bulb, or possibly like a small hand-operated bike pump, with a hose on each end. 



An arrow or other marker will be present on the bulb to show you which side is the intake and which side is the outlet. You simply submerge the end of the intake hose, put the end of the outlet hose at some lower point (in your case, out the window), and repeatedly squeeze the pump until it has pulled water up to and through the pump and water is flowing freely. Once the flow is established it will siphon out all the water (until the water height is equalized, which won't happen in your situation).