I learned these way back when I was a Brownie Scout, and the basic lesson was a good one: the weaving skills, however rudimentary, came in handy when I purchased three seatless but otherwise fine porch rockers. I used clothesline and this same technique to fashion new, comfy "sit-upon" seats for them. Other grownups marvel at my creativity, but I shrug and think of these old newspapers.
Take a page from the newspaper and fold it over and over again so that it makes several long strips, about 1 1/2 to 2 inches wide.
Lay seven or eight strips across horizontally in front of you on the table. You want to have a series of strips about 18 inches wide all together, with very little room in between.
Take one strip and hold it vertically over the left (or the right, whichever you prefer) of the series of strips you've just laid on the table.
Place the top horizontal strip OVER the vertical strip.
Place the next horizontal strip UNDER the vertical strip.
Place the next horizontal strip OVER the vertical strip.
Keep alternating until you run out of strips.
Take the next vertical strip, and slide it next to the first vertical strip, nice and tight, but this time, alternate the over and unders -- the first horizontal strip, for instance, will go UNDER the vertical strip, and the second will go OVER the vertical strip.
Repeat until you have woven your way through about two feet of strips. You should have a mat about 18 inches high by about two feet wide.
By now, you'll have strips hanging off on all sides. Trim them and tuck them snugly into the folds.