Instead of trying to tether the Moon, can we somehow harness the Moon's kinetic energy, the same way we do wind? If so, how is this possible?
Sure, it's possible, as most things are. It's not plausible, though, and a very not good idea™, unless you intend to wipe out our planet.
In essence, there is no such thing as "free" energy - energy has to come from somewhere, so if you take it from the moon, and transfer it somewhere else, the result is that the moon has less kinetic energy. In an orbital system like the Earth and moon, lowering the kinetic energy of the moon would cause it to orbit the Earth closer, quickly resulting in stronger and potentially destructive tidal forces, and eventually resulting in the moon crashing into the Earth (if you kept harvesting energy from it). You also run the risk of creating an unstable orbital system, which in the long term would result in the moon either "being ejected" from Earth orbit, or again, crashing into the Earth.
Furthermore, long before developing the technological capabilities to harvest the moon's energy, we'd have a much better energy option anyway, in the form of large solar panels harvesting the vast energy output of the sun, for an example we can easily envision today - and the future may well bring even better options we can't foresee, as it tends to do.
As to how the moon's energy could be harnessed, it would probably be similar to the theoretical models for harvesting the (rotational) kinetic energy of a black hole. The fundamental principle is electromagnetic induction and there are a couple good posts explaining how that would work - one at physics.SE and another at Standford's site. The general approach would be the same with the moon, though as it's tidally locked and doesn't rotate, you take a slightly different approach - imagine a colossal magnet on the moon, and a colossal coil of wire on the Earth (or in Earth orbit). As the moon orbits the Earth and passes by the magnetic coil, it would induce an electrical current in the coil, which could be harnessed pretty easily.
One possible method of using the Moon's motion to generate power is by using a solar sail as a power-generating kite. It's not really harnessing the Moon's kinetic energy, but using the Moon's reliable orbit as a good base and harnessing kinetic energy from the solar wind.