I’m going to be honest, I hate screens. If I owned my own house I would only have screens on the windows I opened regularly and the rest I would leave off. This is because screens trap dirt and I would rather look out a clean clear window then out of a dusty screen. But thats my opinion. If you have screens on your windows, however, you’re probably wondering whats the best way to clean them. There are actually a couple different ways to clean screens. If they are just dusty you could take a damp cloth and wipe them down, I would suggest taking them off the window before you do this as it will cause the dust to get all over the glass. If they are really dirty you could set them up against the house or fence and spray them down with the garden hose, then let them dry before putting them back on. I would not recommend power washing them, they make screens very flimsy now days so a power washer may tear them up unless you have the old metal screens.
Since you have the screens off your windows now would be a good time to clean the tracks and sills. (Do this before you clean the windows) You can use a small brush to sweep out the dirt and dead bugs that got trapped between the screen and the window, now you see why I don’t like screens, or if there is a lot of caked dirt you could spray it off with the garden hose but be careful not to use too much water pressure because water could seep through the window sill and into your house. Then just wipe dry put the screens back on and you’re done. After I cleaned the windows on one house the home owner didn’t even realize the screens where on the window, so clean windows and screens can make a big difference.