I just wash it with the same soapy water I wash the car with. Lightly rub it and towel dry. 2000 C5 , owned since new and top still looks brand new. 85000 KMS.
Same here, wash with car soap, rinse well. Air dry before storing in closed position. Also use touchless car wash in winter and that does a really good job cleaning the rag top. I repeat - touchless.