The ultimate up-cycled chicken nest is here.
Nests can be made from lots of things. But this is the best and it costs nothing!

the best DIY chicken nest should have these features:
• wood free nest to discourage mites
• a smooth round entry hole
• a lip to retain straw bedding, diatomaceous earth, and lavender heads
• plastic so as to be easily wiped out
• opaque plastic to be a cosy dark space
• compact with a flat bottom to slide across the floor for easy access
• a roof, so poop from the roost and mesh floor above doesn’t fall in.

People use plastic buckets and storage boxes, and if you have heaps of room a plastic lawnmower catcher could be good, my chooks always look in if they see a catcher. But there are stories of a snake sleeping off a meal of eggs inside a catcher.

This is my best yet for a small coop.

Get a square plastic food grade drum (best) or oil (wash it well) drum, ideally 300 x 300 x 300mm. A local business is pleased to give me their old ones.
Leaving a roof top on the drum is a bonus as chickens can roost above it and not soil the eggs below with poop.
Because chickens like a small, private and dark place to lay eggs the drum should not be clear plastic but a solid colour.
Flush thoroughly with cleaner.
Cut out the end opposite the handle. But leave a lip to stop the eggs rolling out.
Air thoroughly, dust with diatomaceous earth, put in some lavender heads and add straw.
Face the opening away from the weather.
Rivet a small plastic handle so as to access the eggs if you have a long floors within reach for the eggs.

Chickens are fussy about colour and shape, so put this new one alongside the old one, for the consumer feedback survey. Mine will not use a frosted milky colour.