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)