Microfiber cloth will take all the dust off.
You will first have to vacuum them with the vacuum attachment brush to get the majority of dust off of them and then use a damp cloth and warm soapy water to wipe off each slat front and back. It takes a while. I find it easier to take them down and soak them in the bathtub for a bit and then use a soft hand scrub brush/kitchen sink brush/sponge across the slats before I rinse. I have also taken them out my deck and laid them falt, scrubbed them front and back, rinsed them with a hose and hung them over lawn chairs and deck railing to dry in the sun.
Hi Maggie: If they have a texture to them, then I'd use the brush attachment on the vacuum. If they are smooth, then what you can do is get an old sock and dip it in a mixture of a small squirt of Dawn dish soap, a tablespoon or two of vinegar and a gallon of warm water. Mix this up and put the sock on your hand, make a fist to wring it out fairly dry and wipe the blind slats one by one. You can do both sides at once. Not fun, but at least you can look outside while you're doing this:) Then, get some fresh water and rinse the same way, with the sock hand. And, if you get bored, you can make the sock a puppet and tell the slats how much better they are going to look when they are clean. :) It doesn't take that long, and while you're at it, go do those blades on the ceiling fan:) Good luck