Special paper
The paper used to make bills is not the same paper we use for our everyday needs. US dollars, for instance, are made of 75% cotton and 25% linen, which is why the paper they’re printed on is called "rag paper."
Polymer paper is also becoming popular today. It’s difficult to fake, and even if it looks genuine, it’s very different to the touch.
A good way to tell a forged bill is to apply some iodine: cellulose will react to it, and the stain will become blue.