A rolling four-week archive of 0.25 degree GFS data is available in
Browse the data in your browser at http://awsopendata.s3-website-us-west-2.amazonaws.com/noaa-gfs/
The key layout of data in the buckets is:
FFF represents the forecast hour.
The files are in GRIB format. Within each GRIB file are Climate and Forecast v1.6 metedata that describes the data contained.
There is a general introdcution to GFS at https://www.ncdc.noaa.gov/data-access/model-data/model-datasets/global-forcast-system-gfs