  We explain the entire process by which we conduct the Galactic Arecibo L-Band
Feed Array HI (GALFA-HI) survey. The survey is a high resolution (3.4'), large
area (13000 deg^2), large Galactic velocity range (-750 to +750 km/s), high
spectral resolution (0.18 km/s) survey of the Galaxy in the 21 cm line
hyperfine transition of hydrogen conducted at Arecibo Observatory. We touch on
some of the new Galactic science being conducted using the GALFA-HI survey,
ranging from High-Velocity Clouds to HI narrow-line self-absorption. We explain
the many technical challenges that confront such a survey, including baseline
ripple, gain variation and asymmetrical beam shapes. To correct for these
systematic effects we use various newly developed methods, which we describe in
detail. We also explain the data reduction process step by step, starting with
the raw time-ordered data and ending with fully calibrated maps. The effects of
each step of the data reduction on the final data product is shown
sequentially. We conclude with future directions for the ongoing survey.
