There, science information is separated from engineering data and routed to DCF, the Data Capture Facility where error-checking systems verify signal quality before it's recorded and relayed on to the Space Telecope Science Institute.
At STScI the signals are checked once more to ensure the observations were correctly performed. The raw data is re- calibrated to compensate for known variations in the instruments.
Final science data is recorded on optical discs, each the equivalent of a dozen CD-ROMs, for archiving and distribution to the astronomers who may have first designed the observations years and months before!