Communications between the Earth and the farside of the Moon is challenging, and currently impossible, because there is no line of sight between the Earth and the far side.
Optical Fiber Cables
One option would be to install a large fiber optic cable across the lunar surface to a repeater station on the lunar limb.
Chain of Microwave Towers
Communications relay satellites
There are various proposals for communications relay satellites, but it is a difficult problem to solve. Earth has geostationary satellites which are in stable orbits, hovering constantly over a point on the Earth's surface. Unfortunately, unlike Earth, the Moon has no equivalent of geosynchronous orbits.
There are at least four options available for relay satellites.
Option 1) Located at Lagrange Libration points
The problem here is that the Lagrange points are many tens of thousands of kilometers from the lunar surface, which results in large space attenuation, adversely affecting the respective link budget, and introducing more round trip time delays.
Option 2) Molniya Satellites
This option would be to have a large constellation of several Molniya type low orbiting relay satellites in elliptical polar orbits.
Option 3) Halo Orbit Satellite
The halo orbit about the Earth/moon L2 point is roughly a circular path in the Earth/moon reference frame. The path lies in a plane perpendicular to the line going through the Earth's and moon's centers of gravity and about as far from the moon as the L2 point. The Earth and the far side of the moon can both be constantly visible from such an orbit. However the halo orbit is not dynamically stable so repeated stationkeeping adjustments would be required to maintain the orbit.
Option 4) Lissajous Orbits
Lissajous orbits about L2 are also not dynamically stable and differ from the halo orbit in being differently shaped non periodic paths about the L2 point.