There is all sorts of information online regarding how to braid a rag rug, so I've distilled down the easiest way of making one in, hopefully, an easy to understand set of instructions.
The instructions that follow are for making a braided rug using three strands. If you know how to braid using 4 or more strands, by all means, go to town. You would just need to create that many long strands for your project.
A quick note about the width of the strips: if you are using heavier fabric, you'll want a thinner width (close to 1" wide); if you are using a thinner fabric (like old t-shirts), a width of 3" will be more ideal. Just be consistent and keep the same width throughout, unless you want a lumpy rug.
Strips of rags cut into 2" wide lengths (the longer the better)
Sturdy thread (quilting or carpet thread is ideal)
Thick needle or curved upholstery needle
Prepare the Strips
There are several methods to joining the strips of rags together. You can sew them together (on the diagonal) or you can knot them together. Basically what you want to achieve is three very long strips of cloth. If you knot them, the knots may be visible in the rug, so if you are using thicker cloth, sewing may be the way to go.
The longer your three strips end up being, the larger the rug. But you can always clip your work and sew more strips on later if braiding with really long pieces is driving you nuts. Anything over 8 or 9 feet is difficult to braid. So, add on as you go.
To start, sew or knot the three strips together. You can attach the start to something heavy or have someone hold the end for you while you braid. This can be fun for kids since they get to help out and watch the process while they are at it. Once you've braided far enough down where it doesn't twist, you won't need your helper. When you reach the end of your braid, sew or knot the loose ends together.
Sew it Up
Coil your braided rope on the floor, starting at the center for a circle. If you prefer an oval shape, start with one foot length and coil around that. As you coil (or when you are done if you want to check the shape), sew the rows of coil to each other, lacing them as shown in the picture on the right. When the coils are secured tightly, fasten off.
A small or medium size rug is ideal, because you can clean it in a washing machine without too much of an issue. I'm planning on making some bath rugs for the kids with a bag of old clothes!
If you are a more visual person, here's a video instruction of basically the same method:
Braided rug making instructions
A brief history of rag rugs
How to make a flat braided rug