I came up with this idea as I wanted to make a rug quickly and by not using any sewing or special tools. This one (about 40x30cm) was done as a test and took 3 hours to complete. It's all made from old fabric so it cost nothing to make.

Step 1:

To make a rug that is 30cm wide, I used 3cm wide strips of thick cotton fabric, each being about 75cm long.
You then fold a strip in half and tie loose knots all the way down, finishing with a tight knot at the end. You need loose knots so that you can thread more strips of fabric through later. It's not important to make sure each one has the same number of knots but more or less the same is fine as I'll explain later.
To grip it, I simply held the folded end in my teeth and tied the knots. ;) You may want to hook it over something.

Step 2:

I ended up with 19 strips when I ran out of this fabric. The next thing is to make the strips to loop through the knots. I used white to show the different parts but of course it's up to you if you want to make a pattern or just use a solid colour.
I used white, thinner cotton, also 3cm wide but longer. Line up the knotted strips and see how long it is across then cut your secondary strips 2 and a half times longer. Mine was 40cm across so the white strips were 1m long.
First, you need to tie a tight double knot to the red strip at the corner. As you can see in the second photo I started with the edge that had the folded parts of the fabric. Then, thread it through the next strip's hole, bring it over and thread it through again so that it holds on. You can't see it in this pic but each of them are looped over. Pull each loop quite tight or the rug will be like one of those expanding net-bags!
When you get to the end, tie another double knot to secure the first row.
Then do the same at the other end so you've got the edges all secured.

Step 3:

Next, I threaded one through the middle just to get it holding together well. This also helps you to see how many knots there are and where to thread your next strips.
I used 10 white strips altogether. As I continued I could see which holes were close together and a few got missed out but when it becomes more tightly made you can't see those that weren't used. If you find you don't have a hole available, just go on to the next column and thread it through that one. It won't show up.
As this procedure is so simple, it doesn't take much time at all. I think I did all the loops in 1 hour.

Step 4:

This is the view of the other side so you can see that you have two different faces, should you wish to use the face that doesn't show so much of the other coloured fabric. I chose to have it loop-side-up, if you will, as there was one rogue loop showing at the top edge in the middle! :)
So, a rug made just from tying and looping that is quick and really easy to make. I know this one looks a bit rough but it was my test one just to see if it would work.