Be sure to vacuum really well first as this will lift dirt out and lift fibers up a little. Spraying any kind of liquid onto fabric acts to draw any dirt deeper into the fabric, so remove what you can with a vacuum first.
Blot out excess water using a clean, dry towel or even something like a synthetic chamois, something that absorbs water well.
To dry faster, place an electric fan in the car so that it blows onto the sets, just having an air-current inside the car will speed up evaporation.
I'm sure others will chime in with their tips and techniques...