Safe techniques

Generally the areas that require cleaning have the material looking dull and the pile lying flat, held down by the grime and sweat that builds up when you drive. You'll most commonly find this on the steering wheel and the seats.   

The first step is to vaccum the entire fabric surface, to remove any dust, dirt and heavier particles. For effective cleaning, use the crevice tool held at a slight angle away from the suface. 

Now closely inspect the fabric, look for potential stains and other marks in it. You want to identify and remove these marks first, as you don't want to be rubbing any grime from them further into or across the material (called stain migration) while you're cleaning it. 

Work on small sections at a time, like a seat bolster, one side of the steering wheel etc, before moving on to cleaning the next section. You can do the entire fabric surface for the last two stages in this article (vacuuming and brushing).