Vacuum them. If really dirty, blot carefully with really hot tap water using a jumbo car wash type sponge.
Try a vacuumed first to get all the dust of then get a bucket with hot soapy water and wash them down then get clear water and rinse and they will be nice and clean if you don’t vacuumed the dust will come in the house.
You can use a pressure washer, just make sure your windows are closed.
There is a spray you can connect to your garden hose. https://www.amazon.com/Windex-Outdoor-Glass-Patio-Cleaner/dp/B01MUFTH05/ref=asc_df_B01MUFTH05/?tag=hyprod-20&linkCode=df0&hvadid=309944394874&hvpos=1o2&hvnetw=g&hvrand=3544590371528195192&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9030432&hvtargid=pla-574541404692&psc=1&tag=&ref=&adgrpid=62022137216&hvpone=&hvptwo=&hvadid=309944394874&hvpos=1o2&hvnetw=g&hvrand=3544590371528195192&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9030432&hvtargid=pla-574541404692
On the inside, just wipe them down with hot soapy water and use a butter knife if you need to get the screen crevices cleaned.
Then hose them off on the outside of the house.
As others have said, I've had luck vacuuming dirty window screens. That's probably the easiest thing to try at first, and if it doesn't work, you can give some of the other suggestions a shot!
Try this: https://www.hometalk.com/16277883/window-screen-cleaning-tip
Yes a pressure washer used from the outside. Make sure your windows are closed and you don't have any leaks within the windows that the water can get inside both panes of glass. If the windows are fine, use the pressure washer right on the screen and see the dirt drip out:)
Yolanda...we use pressure washer with Krud kutter from Lowe's. Good luck
If you use a pressure washer be careful not to have it on full force, it can break a window. I also put a towel on the windowsill inside, because my window have little vents to let the water out when it rains. I use Dawn Premium with my pressure washer, You could try Purple Power degreaser from Walmart, and try to do it on a cloudy day, so the windows do not streak while cleaning the screens.
Vacuum first to remove all dust and grime. Wash down with a mix of warm water, baking soda and vinegar and rub over with a cloth. Use a clean dry cloth to dry if necessary. Be gentle. Do not press too hard as to loosen the screen from the sides.