Step 1: Supplies and Tools
Styrofoam Cooler - I got the cheapest one I could find from Wal-Mart for about $5
Tape - the stronger the better, I would suggest duct or packaging tape. Something that could hold up to some abuse outside
Insulation - Batting or Packaging Peanuts work great and are easy to find around the house. You can use Hay or Shredded Newspaper too. However some cats are allergic to Hay. It is important that whatever insulation you choose, it not be rigid or unable for the feline to burrow in it.
Plastic Bags - So the insulation does not got moldy from moisture I'm putting it in plastic bags.
Scrap Fabric - For added warmth and burrowing capabilities inside the shelter I used some scrap fleece I recycled. A old pillowcase or cotton fabric works great as well.
Adhesive (Optional) - make sure it is suitable for use with styrofoam