Vacuum and then spray an all-purpose cleaner onto a clean cloth and rub it on the spot. Never spray a cleaner directly onto a slat. Rinse by rubbing a cloth moistened with clean water over the area.
I found professional Dry Cleaning kits on Amazon for use on my find large area rugs, so that it will not be necessary for me to take them outside on my concrete patio and subject them to the heat and water of my steam vac.
Most times they are only dusty and not dirty so you could use the small brush from the vacuum set to vacuum them. If they do have some marks, use a damp cloth dipped in warm water, dish liquid and baking soda to remove them.
I purchased my solid beige fabric vertical blinds for $5.00 back in 1991 from a local department store going out of business. Back then we needed something to hang over the 6 ft sliding doors in our sunroom for neighbor privacy. About a year ago we repainted the sunroom and those dusty, dirty blinds needed refreshed too after hanging there so long. I took out the weights, removed the panels off their plastic hanger thingies, put them in the washer (one that does not have an agitator) with Woolite on a gentle cold water setting, then into the dryer on air setting for a few minutes before hanging them back up to dry and replacing the weights in the bottoms. We had also replaced the old carpet with wood-look flooring which raised the floor height so I needed to hem each panel. I used regular iron-on hemming/fusion tape to hem the bottom of each one - which took a while to do. Since I had removed the blinds to do that and had the iron out anyway I also lightly pressed the slight wrinkles out of each panel. My 27 year-old vertical blinds are now hanging about an inch off the floor and look darn near brand new again.
I gave up on this: Had textured ones that were old & grubby, plus there was always cat-hair from rubbing against them. I interchanged into the original fixture with new vinyl S-curves. Very happy now.