RDF systems are pretty easy to understand. Simply, the operator tunes to a radio station that has known coordinates, A directional antenna is used to get a bearing to the radio station. The procedure is repeated with another radio station. The operator's position can then be calculated.
Hyperbolic systems are a bit more difficult to understand.
A hyperbolic system uses coordinated transmissions from two or more radio stations. The user uses radio equipment to listen to the radio signals, then matches the difference heard to the appropriate hyperbola on the map. This puts the user somewhere along one arc on the ground. This process is repeated by using a second pair of stations to determine another hyperbola. The user determines position by finding the point on the map where the two parabolas intersect.