I use either a convt top cleaner which is just soap but I bought it anyway, or I just use car wash soap and a very soft hand brush. I have one that has very soft bristles and it gets all the dirt and dust out of the top that a sponge cant get.
Porsche makes a very nice cloth top cleaner, and that is what I use on my car. It is mild yet effective, and very gentle to the fabric/stitching.
My top does not see alot of dirt/grime so I use a closed-cell sponge, but if you need something more aggressive then a soft bristle brush is acceptable.
I have found an Absorber to do a very good job of pulling the majority of the water out of the top after washing. Following the Absorber, I go over the top with quality microfiber towels to pull the remaining water out. Never fold your top down until you are certain it is 100% dry.
You will also want to be sure to treat the top with a protectant as needed. Ideally, a cloth top should always bead water and not absorb it. Treating a top with a cloth top protectant will not only offer UV protection to the material, but will make subsequent cleaning easier as it offers a barrier to dirt. Use your best judgement as to the frequency of applying a protectant - factors such as outdoor vs. indoor storage of the car, top up or down most of the time, daily driver vs. garage queen will all play a role in the frequency of applying a protectant.
Both 303 and RaggTopp make a nice cloth top protectant that should serve you well. Take your time, it's worth the effort.