I was born in the 50's so I grew up using a pressing cloth. You use it on material that shouldn't take direct heat. When I used it, I would get my pressing cloth wet and then wring it out before I put it over the item on the ironing board.
I still use a pressing cloth. I like to use the old type of dish towels. (The ones that were like muslin. I agree that the muslin might be too thin so if you do use muslin, double it for protection.