1) 8 half-size sheets of newspaper or 4 full size sheets
I used the advertisement section for the colors; extra is good to have for covering your work surface.
You need something that will dry clear and is easy to apply. I used Scotch brand scrap-booking glue, which came in a tube with two applicator tips, one small and pointed, one round and fabric for smearing. I found this fabric side to be the most helpful for applying thin coats of glue.
4) needle (& thimble)
The eye of the needle needs to be big enough for whatever string you choose, but otherwise the needle should be as small as possible to keep from making huge holes in your final product. You may also want a thimble to protect your fingers while pushing the needle through the paper rolls.
5) thread or string
I used #20 red hemp cord, which I had on hand, but probably picked up in the beading section of a craft store at some point. Other good options would be cotton twine or sturdy button thread (probably doubled). This is mostly an aesthetic choice.
Step 1: Prepping the Newspaper
Fold each strip in thirds lengthwise. Just this first time, you don't need to glue down the flaps. As you fold, you are choosing which colors will end up on the outside - whichever colors are in the center on the outside (you are folding away from the outside) will be the color of the rolled paper unit.
Then fold each strip in thirds lengthwise again and glue in place. It helps to fold first to get the creases straight, then unfold, apply glue, and press together. Using a fingernail to get your creases really crisp at this step makes the final fold easier.
Repeat the folding in thirds and gluing one more time, so that you have long strips of folded newspaper about a quarter of an inch wide. This is possibly the most difficult step, since you are folding several layers of gluey newspaper together. Don't expect to get past this step without sticky fingers...
Step 2: Roll the Paper Strips Into Final Shape
First take a look at the colors of your strip, and decide which end you want to have on the outside of the unit and which you want on the inside. Starting with the inside end, pinch an inch or so and roll it up tightly. It's important for the first rolled-over piece to be as small as possible, or you will end up with a rectangular unit instead of a square when you're finished. (There's nothing wrong with rectangles if that's what you're shooting for, but if you want to end up with a square then unevenly-sized rectangles will be tricky to fit together to make a square.)
Unroll that inch or so and apply glue to a small section of the strip. Re-roll the inch and keep going until you get to an unglued portion. Then glue the next 6 inches or so and keep rolling. Repeat until you reach the end of the strip.
As you roll, do your best to make regular square corners. Some squishing and pushing around is definitely involved here, but the sooner you get it square the easier it will be to keep it that way until the whole strip is rolled. Perfect corners are not as important as straight sides.
Do all 16 strips like this, and then arrange them however you like to make a nice pattern for the final potholder. Leave them until the glue is completely dry and the units are hard little squares, probably several hours at least (I left mine overnight).
Step 3: Sew the Units Together
Thread the needle, no knotting is necessary. Push it through the edge of one paper unit, between the two outermost layers of the paper roll and at the center of one side of the square. Pull it through so that you have an inch or two of string left hanging out the opposite side of the square.
Then in the same way push the needle back down through the edge of the next unit in your array. When you turn the two squares upside down and remove the needle, you now have two loose ends of string coming out of two adjacent paper units. Pull them tight together and tie a simple overhand knot. (See the second picture in this step.) The side of the units with this knot will end up being the back side of the final product.
Holding onto the loose ends of string, flip the connected units over again. Wrap the ends of string around the single string that's there already, just crossing them past each other.
Finally, flip over to the back side again and tie the ends of the string together tightly into a square knot. Trim any excess string.
Repeat to connect the rest of the paper units together. I found it easiest to first make four strips of four units each, and then connect these. Just make sure you're keeping the knots consistently all on one side of the units, so that you end up with a smooth front side.
You now have a sturdy and heat-resistant potholder! Of course, you could use those paper units to make just about anything you want...use just 4 units for a coaster, 96 for a placemat, or a whole bunch to create a pixelated image and hang it on the wall.