Best I have ever done with them is to put a few inches of hot soapy water in the bath, place the blind in and give it a bit of a soak then use a cleaning cloth to rub each slat to remove any stubborn dirt and dust, drain the water then dry the blind from the bottom up with absorbent cloths and finish off with a hairdryer so that the strings get dry
My mum used to lie in on the tiled floor in the bathroom and spray it with the shower head and some washing up liquid. Then hang it on the shower rail or outside in the sun to dry.
These were plastic venetian blinds, don't know if you could do the same with wooden ones