Radians are easy.
Picture an angle whose vertex is in the center of a circle. An angle of one radian is one with rays subtending an arc equal in length to the radius. That's the basis of the measurement, the equivalence of the arc length for such an angle with the radius.
2pi radians measures an angle that goes all the way around. This follows from the fact that the circumference of the circle is 2 pi r. The conversion factor is 2 pi radians per cycle.