The simplest of all the designs, it is just a projectile (armature) located between two rails. As power flows from one rail, through the projectile, into the other rail, a force, known as the Lorentz Force, pushes the projectile forward.
Critically, and unfortunately, the rails and the projectile have to be in physical contact for the system to work. At high power levels and high speeds, the arcing, plasma and wear creates limits on the number of times such a launcher can be used without needing to be rebuilt.
In fact, the DoD quietly shuttered their research effort into high power and high-speed rail guns as the issues with robustness at high power levels and high speeds do not appear to be resolvable.
There are experts of the view, once freed of tactical constraints such as short barrel length, the rail gun could still possibly produce a workable space launch system. Careful attention to managing the plasma, and power introduced along the full length of the launcher rather than solely at the base, could possibly produce a workable way forward.
Further, there are proprietary hybrid designs combining rail gun simplicity with novel magnetic levitation methods that could also help with the fundamental difficulties of the rail gun approach.