Like magnet on Moon and coil on Earth , as in motor where magnet revolve around coil ..(Notice that it's an idea behind it; I don't want to cover earth with coil and moon with magnet or vice versa; main thing is how to use natural rotational or magnetic behavior) am I right, or we use Earth's rotation itself.
Yes, you can usually 'steal' power via the magnetic field of a planet.
If your planet has a magnetic field, and the orbiting thing (moon, satellite, spacecraft) has a path that crosses the flux lines of the magnetic field, then one can extract energy via a conductive loop or coil.
The stronger the magnetic field,
the bigger the loop area (times the number of coils),
the faster the orbital velocity,
the more the orbital axis lines up with the axis of the planet's magnetic field,
the more power you get. But note that the energy comes from the orbital kinetic energy of the orbiting body. So small orbiting satellites should only steal power if they're OK with decaying their orbit (e.g. to re-enter.) IMHO, far-thinking people should avoid decaying the orbit of a massive satellite, just for some cheap power; that's unlikely to end well for those on the planet.
On the other hand, as in the story cited below (readable online), one can put in power -- and boost the orbit. This can be useful, since that boost doesn't use any reaction mass!
Tank Farm Dynamo" by David Brin
or if you want the physics, math (and IMHO some good, helpful illustrations:
Physics 8.02 Electricity and Magnetism: StudyGuide
I suspect there's a corner case, with just the right orbit about nonrotating planet with a magnet field (one lined up so as never to cut the flux lines of the field) wouldn't generate any power. However, nonrotating planets usually don't have much in the way of magnetic fields.
Under normal geophysics of planets with molten metal cores (like earth), there's usually strong linkage between the planet's rotation, core and field Except during pole-reversal events, in which case, the field will probably be too weak to get anything useful out of it.
The moon produces tides. One can harness water level changes from tides to produce energy. So: indirectly using moon energy. I thought that this had been going on for years in places like the Bay of Fundy where there are huge tides. I was surprised to find this link stating that only recently has there been successful implementation - it is tricky.
We would use something smaller that cost less and is easier to maintain. Like inflow generators.
Have in mind that generator that would use force of earth or moon would need to have relative large size. It would also generate relative large amount of energy. You would need to calculate the amount of copper and magnets needed to create generator that would be large enough to be affected by earth magnetic field or earth-moon movement.
Also you would need to take into consideration the fact that orbit is elliptical so all calculations would need to be done for the closest proximity between planet and moon(s) so your generator would not work 100% of time or would not produce the same amount of power all the time
If the satellite is a smaller, artificial one, it can be closer to the planet. If the planet has a magnetic field (ie. Earth and Jupiter but not Venus or Mars), you can drop a long wire behind the satellite and use an induction effect. This will also drag the satellite, lowering its velocity so it would need to spend fuel to maintain orbit. I think we use it now in reverse, as a motor instead of a dynamo.