We don't have a tremendous amount of information here on reducing data from FPs, a reflection of lack of abundance of these instruments. For the very basics about using FPs, please read the corresponding section under observing-techniques. Details on reducing data from FP spectrographs can be found on this page, hosted by the University of Montréal. There are links to IDL codes for reducing FP data and a user manual (which may be in French), and links to surveys that used FP data. The instrument this web-site was written around is FaNTOmM. Much useful information can also be found on the web-site of CFHT, in a user manual of the now decommissioned Scanning Fabry-Perot Spectrograph. (Hopefully CFHT will not decommission these web-pages as well.) Although the user manual is for a particular instrument it is well written and you can learn much about FPs in general.
FPs have been used in a number of galaxy surveys (e.g. SINGS), as mentioned on the Montréal web-site, and so if you want to know more we would recommend an ADS search on the literature; we can direct you to Daigle et al, 2006, MNRAS, for example.
The main step in the reduction that is different from other IFUs is the phase correction. The steps working on extracting the data itself from the detector will be much the same as for imaging work: each raw frame is basically a narrow-band image with wavelength changing over the FOV. By scanning the whole FSR (free spectral range) and due to the cyclic nature of the interferometer (which is the heart of an FP spectrograph), the flux in the different channels for each pixel can be shuffeled around to construct a uniform wavelength axis in the z-direction of the cube (and hence create a data-cube with 2 spatial axes and 1 spectral axis). The phase-shift (wavelength-shift) over the FOV needs to be calibrated (usually before and after each target exposure) by observing an emission-line lamp. From this, one can measure the phase-map needed for the phase-correction of the science-data.
After that, you have a data-cube which can be further treated, e.g. measuring and subtracting sky-emission from empty regions in the FOV.
IDL-based data reduction package for FP data can be found here.
If anyone has a lot of experience observing with and/or reducing and working with FP data, it would be useful if you could add your knowledge here. It would be nice if this section was as complete as that of the fibre-fed IFSs.