You can't generate power from a static magnetic field alone. In this context, the earth is just a permanent magnet, and a rather weak one at that. To generate electric power from that, you have to move electric conductors, like wires, thru the field in the right direction and with the right orientation of the conductor.
If any electric power is taken from the resulting EMF produced by the moving wire, then a force will be required to continue moving the wire. Put another way, the wire will "push back" as you try to move it thru the magnetic field. That push times the velocity represents power you have to put into the system to get the electric power out. Power isn't coming from the earth.
You can get the same effect by passing a wire thru the field created by any other permanent magnet. The reason this is usually done instead of using the earth's field is that a deliberate magnet can easily have a much stronger field, although much smaller in size. You can also get the same effect by holding the wire still and moving the magnet, which is not a option when using the earth's magnetic field. In the case of moving the magnet, it will require force to move past the wire when electric power is drawn from the wire.
There is no free lunch here, and any claims to the contrary are just bunk and a waste of time to persue.