How do you build a greenhouse cheap?
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Free pallets some nails and heavy duty plastic
You can build the frame using 2x4 lumber and simply cover with vapour barrier.
2 x 4 frame is best because it's going to be sturdy and then cover with plastic. Here's the thing with plastic it doesn't stand up to heat and wind so you'll have to replace it within a year. So closing in the frame with hard plastic or old windows might be a neat option. Maybe seek craigslist for recycled materials.