I have not done it lately, but I used to be the Queen of rag rugs. The method I used was the thick crochet hook method already mentioned.
I had mixed success with my rugs. What I found is that it really mattered what material you made them from. For one thing, you cannot mix types of material. I used several different types of fabric but found heavier fabrics made flatter carpets that held up better. It also worked better to make rectangles that were no larger than bath mat size....if you made them round or large there was no way to keep them from slipping around or just not lying flat. Single crochet is all you need to do and crocheting that big could not be simpler.
However they made excellent bath mats especially when made from old towels. You just wash them however you would wash the fabric you make it from. Rugs made from stretch fabric were nice looking but impractical because they would slide around on the floor dangerously.
They do have a very "country" look so if that isn't the style you are going for it probably isn't a good choice unless you use an interesting fabric.