One of the most direct ways of getting a sponge to that outside window is with an aluminum extension pole. The tool, available at hardware stores, is either a telescoping pole, or one that comes in pieces that you fit together, with a sponge at the end. It will reach 15 to 20 feet, which should be plenty for a second-story window. The best cleaner to use is a mixture of one part ammonia to four parts water---it dries quickly and minimizes streaking.
If you have good water pressure in your garden hose and good aim, consider buying a spray cleaning system that attaches to the hose. It's a bottle with an attachment on one side where you insert the hose and a spray nozzle on the other side. The bottle contains a concentrated anti-streak cleaner that mixes with the water from the hose as you spray it, sending the solution in a pressurized stream up at the window. Start by aiming at the top portion of each window, then work the stream downward in a back-and-forth pattern to rinse.
The best high-window cleaning tool you can get is the window itself. If you're considering installing new windows at any point, make sure that the upper-floor windows are double-hung (meaning both the top and bottom sashes move) and that the sashes are designed to drop inward on hinges for easy cleaning. All you do is squeeze a release lever to drop the windows inward, so the outside of the panes are facing inward, then wash with glass cleaner and paper towels.