Before gathering the physical supplies, you first need to gather the knowledge. Go here
to learn how to fold a hyperbolic paraboloid. The link is from Erik Demaine's website. If you would like to learn more about the math behind this structure, check out this page
Things you will need for this instructable:
24 sheets of square paper - The color does not matter. I color coded the sides for this instructable to make it easier to see the different sides of the finished "cube". Also, if you can, use good paper. It's completely possible to use cheap paper for this, as I did, but it will be much sturdier if you use good quality paper.
Double-sided tape - This is the best method I could think of for attaching the hyperbolic paraboloid units together. You could use glue or some other tape, but I highly recommend double-sided tape.
Thread, a needle, and masking tape - This is optional and only needed if you plan on hanging your finished sculpture.