Check with the manufacturer or owner's manual to be sure, first, Madonna, but I have vivid memories of my mother taking down horizontal slat blinds and washing them in the tub. Gentle soap, swish them around, check both sides for stains or remaining dust. Then a fresh tub of cool water for rinsing. My mother just hung them in place to dry. Towels and newspapers caught any drips. I was on the towel brigade.
Every room in our house had slatted blinds so her spring cleaning lasted a looong time... The only one that gave her fits was the 6 ft picture window blinds in a 5 ft tub. I don't remember how she did that; it was best to stay in another room when she was tired. ; )