This is not my brainchild, I've seen it several places (like here), but I thought I'd share how I did it, step-by-step:
1) Find a magazine. The latest Gudrun Sjöden-catalogue worked great, as the pictures coordinate colorwize. You'll need a ruler or tape measure and a pair of scissors, and a small stapler or double-sided tape is also handy.
3) Fold the strips lengthwise - first in half, then each flap is folded towards the middle. Each strip is now about 1.5 cm wide:
5) After weaving 7 x 7 strips, I folded the exposed strips upward to form the sides of the basket, and continued to weave the sides. At this point, I used staples to hold the strips in place.
Each strip isn't long enough to go around the entire basket, you'll need two:
6) After weaving to the top (I used 4 heights of strips), trim the top edges so they align.
7) Lastly, fold a strip over the top and fasten with staples: