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The Faint Infrared Grism Survey (FIGS) is a deep Hubble Space Telescope (HST)WFC3/IR (Wide Field Camera 3 Infrared) slitless spectroscopic survey of fourdeep fields. Two fields are located in the Great Observatories Origins DeepSurvey-North (GOODS-N) area and two fields are located in the GreatObservatories Origins Deep Survey-South (GOODS-S) area. One of the southernfields selected is the Hubble Ultra Deep Field. Each of these four fields wereobserved using the WFC3/G102 grism (0.8$\mu m$-1.15$\mu m$ continuous coverage)with a total exposure time of 40 orbits (~ 100 kilo-seconds) per field. Thisreaches a 3 sigma continuum depth of ~26 AB magnitudes and probes emissionlines to $\approx 10^{-17}\ erg\ s^{-1} \ cm^{-2}$. This paper details the fourFIGS fields and the overall observational strategy of the project. A detaileddescription of the Simulation Based Extraction (SBE) method used to extract andcombine over 10000 spectra of over 2000 distinct sources brighter thanm_F105W=26.5 mag is provided. High fidelity simulations of the observations isshown to significantly improve the background subtraction process, the spectralcontamination estimates, and the final flux calibration. This allows for thecombination of multiple spectra to produce a final high quality, deep,1D-spectra for each object in the survey.

FIGS -- Faint Infrared Grism Survey: Description and Data Reduction