Fluoride ion-selective electrode and ion chromatography are ways to measure fluoride concentration. In the past, colorimetry (spectrophotometry) was often used. More recently, the use of CS-F-AAS spectrometry, with several chemical variants, has been proposed for this purpose.
In the case of water samples, these measurement techniques can usually be applied directly, i.e., without extracting the fluoride from the sample. However, when analyzing soil and rock samples it is necessary to separate the fluoride from the samples, which can be done by a variety of methods. I suggest the interest in steam distillation from acid environments (perchloric, sulfuric, or orthophosphoric), as well as microdiffusion and especially pyrohydrolysis and "pyrolysis" with moist oxygen.
Detailed descriptions of such methodologies and references to original works on the subject can be found, for example, in the monograph W.John Williams "Handbook of Anion Determination", Butterworths Ltd 1979, London or later editions, or in more recent studies by other authors.