A wood stand for a cat hammock can be built from wooden dowels, boards cut to length, or a sheet of plywood or some other material cut to the right shape. You'll of course need the appropriate tools and other materials such as fasteners or glue for the project.
DIY cat hammock with wood stand
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DIY cat hammock with PVC stand
A PVC stand for a cat hammock is built from PVC pipe. PVC is generally used for lawn irrigation and can be put together using a variety of connectors.
DIY cat hammock with improvised stand
Some DIY cat hammock projects re-purpose existing items to function as stands or simply attach the hammock to an existing structure.
Kitty wants Sleep
Some entertaining videos of what cats do when they want to sleep or fall asleep.
Buy or make a cat hammock with or without a stand: premade or DIY
Although you could set up a full-size human hammock for your cat to use, you may want to buy or make a hammock specifically for your cat (it's cheaper and takes up a lot less space). A cat hammock may or may not actually resemble a hammock as humans have come to know them.