How do you make a hydro power generator at home?

If you are just trying a simple demonstration. You use the flow of water to spin a permanent magnet within a coil of metal wire. In hydro-electric projects of a large scale, a water turbine is spun by the moving water.

The turbine is connected to a generator which has a rotor and stator in which a magnetic field is created using an excitation current rather than a permanent magnet If you want to generate power for your home (presuming you have a waterfall nearby), you are far better off to buy a system since, among many other issues, you have the challenge of controlling production to meet your changing loads, and storing the electrical energy to meet peak demand if that exceeds production capacity.

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