This is a work space set up in a small rental apartment's fully carpeted 'living / dining' area. (The plush carpet was brand new. ..and I work with oils, acrylics, inks and other bad things for carpets. EeK!)
Step 1: What you need
HOLLOW DOORS - hopefully second hand and free
2x4's - the same width as the doors to act as spacers (most lumber stores will cut them for you)
BASE SUPPORTS = two things of the same height one for each end.
Almost anything sturdy will work - saw horses, milk crates, end tables, filing cabinets, concrete blocks, etc
(I prefer a height that is just above my knees...so there is room to store boxes underneath. The higher your bottom shelf, the more stable the supports need to be. If you have a lot of paper to store, you could start the shelves at your ankles - leaving just enough room for your feet to fit underneath.)
FREEZER PAPER (optional)
Step 2: Base support
I used plastic pipe* for support. It might have been totally stable if the room's walls hadn't been convex. If I ever used pipe for this again, I would use a wider diameter. (In a permanent situation I have plywood box shelves for supports.)
Filing cabinets, night stands, milk crates or plywood shelves would all make good and probably better and cheaper supports for the doors. Whatever is used needs to support the full width (hinge to doorknob) of the door.
*The plastic pipe and fittings solution was more expensive than I expected. The advantage was in being light weight , small when broken down, easy, and reusable.