Start with a styrofoam pumpkin. Though I've added Amazon links to make things easy, I bought my pumpkin at a dollar store for a fraction of the price.
The first thing you'll want to do is paint your pumpkin white. You'll probably need 2-3 coats of paint.
Once final coat is dry, glue large googly eyes to the pumpkin.
Finally, take one end of the adhesive gauze and secure it to the top of the pumpkin with a drop of hot glue (not totally necessary but it makes things easier for the little ones). Older kids can just hold the end of the guaze in place while they wrap.
Wrap the entire pumpkin, making sure to crisscross strips as you go. Be sure to leave room for the eyes to peek out. When your pumpkin is covered, cut the gauze and secure the end at the bottom of the pumpkin with a little bit of hot glue. That's it...your no-carve mummy pumpkin is ready for Halloween.