Simply, the user 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. The coordinates for the station are ususally published in a book that the operator is user is required to have.
Hyperbolic systems are a bit more difficult to understand.
A hyperbolic system uses coordinated transmissions from two or more radio stations. It relies on the fact that all the points where the difference between radio signals from different stations is constant form a hyperbola. 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.