This article, then, shows how I made my plant hanger and provides all the steps and photos. The whole thing really is a spur-of-the-moment project, though, so keep in mind you could always play around with the knots and let your imagination carry you away.
Step 1: Materials and general tips
Why twine? Why not? Twine has less bounce than the plastic cords, has a nice rustic and rough texture to it, and is easy to work with. I suppose using thin climbing rope would also work, and since it is softer and more supple might also produce interesting results. You'll be paying a bit more for it, though.
The knots and techniques I used for this hanger are extremely simple. I used straight forward three strand braiding and simple knots to keep everything together, although the top section of the hanger was slightly more complex. Refer to the next steps for details.
Finally, I found that it's good to build the hanger around a pot that is slightly smaller than the one you'll actually be using. The twine will stretch a bit once you put the real one in, so this will keep everything nice and tight.