At my school we all made oil-can banjos whcih was great fun.
Just need a bit of wood about the proportions of a guitar/banjo neck, an old oil (or antifreeze etc - basically any gallon / 5L bottle, plastic is best), and something for strings. We used thick fishing line I think, although maybe garden strimmer 'wire' might be better haha
You cut a hole for the wood in the bottle, so that the wood fits tightly through the hole and jams itself in place, near the flat end of the bottle. The flat end becomes the top of the body where the bridge will rest etc.
Make a floating bridge out of a small piece of wood.
Put some nails in at the 'head' end of the neck (underneath, one for each string), and tie the strings one end to that, over end of the wood (= the nut), along the neck and over the bridge, around the bottle and to its handle to locate them. Tuning wasn't really considered but you could jam things between the string and the bottle to make them looser/tighter.
Frets are optional - we marked them with biro by working out where the octave was by ear, and then the 5th, 4th, etc,
I bet you could make a much better job with a few amendments, the main issue being how to tune them, but they were good fun to make, cost virtually zero and the best part was working out where the frets should be by ear. Learnt loads from that.