Best method I found for cleaning cloth seats (without a professional steamer or shampooer) is to vacuum and brush the cloth first, to get rid of surface dust etc. Then mix a strong solution of carpet shampoo (1001 or something similar) with water. Whisk this to produce a froth on the top of the liquid. then using a stiff nail brush or similar dip in the froth - taking only minimal water on the bristles and scrub the pile with the froth. Make sure if there is a nap to the cloth that you brush it in the right direction when you finish or you'll end up with swirls or odd patches when it dries.
When the seats are dry, vacuum again. Any remaining stains re-do with a wetter brush but watch out for over -soaking.
Oh yes - of course - test a bit that's out of sight first. Good luck.