I want to make a large rug for my large living room.

https://www.hometalk.com/diy/decorate/rooms/diy-area-rug-613578?r=2

A long time ago, I had a bunch of rags-good clean rags of similar fabric type. I cut them and then tore them into strips about 1" wide, next sewed them together lengthwise (end to end) and rolled them into a huge ball. From there, I crocheted them into a circle-my new rug. Original and 100% washable. No one had 1 like it, many compliments.

you could buy a piece of vinyl that is the right dimension for your room. Turn it over and paint the rug of your choice! You could also make either a braided rug or a hooked rug, but I don't know how to do either of those.

Braided rugs are easy to make if you know how to braid. You will need though a large volume of old fabric that you can cut into long strips, and large sturdy needles to sew the braid rolls together with. Some 'modern' fabrics such as polyesters and knits do not work well for making into braided rugs, as they are too slippery, and the fibres do not cling togther well enough to ensure that the braids stay intact.

The best fabrics are cottons, wools, and blends. Shiny, satiny or stretchy fabrics with lycra are not recommended. Nor are fabrics that have a high fray factor, such as denim. You can minimize the fraying by cutting the strips wider, then folding them in on themselves before braiding, but this requires patience, and it works best if they strips are all cut to an even width with a rotary cutter.

One source of inexpensive fabric is thrift stores - bedding, curtains, clothing.