A Mobius strip is one of those interesting things for which there is little use other than starting an argument :-)
- paper (ideally construction or other thick paper)
It should take about 10 minutes.
Step 1: Cut a strip off paper
Cut a reasonably straight, parallel strip of paper. I cut about 3/4"(~1.5cm) off the long edge of a piece of letter size (~A4) bristol board paper, which worked well.
It isn't important how wide the piece is, but you want to get the long edges reasonable parallel, especially at the ends so the widths line up for the next step.