View the the links to AMIP, NOAA/NCEP/NCAR, NASA/DAACs, ECMWF, et cetera in the primary document page. For archived observations, go to NCAR and NCDC. For analyses/reanalyses,forecasts, go to NOAA/NCEP(NCDC), ECMWF, and the GSFC DAAC. The answer to the second question also lists key sites.
Sometimes you can ftp download, sometimes you order (and maybe pay a lot for) CDs. We at the DAO have obtained an archive of tapes that were assembled by NCAR Data Support Section http://www.scd.ucar.edu/dss. For real-time data that's used for weather analysis and forecasting, conventional data are assembled under the Global Telecommunications Network. Satellite real-time data are assembled and retrieved and distributed by the National Environmental Satellite, Data, and Information Service (NESDIS). In the future, Earth Observing System (EOS) satellites will be used for providing real-time data for climate analysis as well as for reanalyses. These include data for both regular meteorological analysis, such as wind, temperature, and moisture, and also other variables such as ozone that are of general interest to earth scientists. This will be coordinated under the EOSDIS Core System (ECS). The DAO's real-time analysis data, it's reanalysis data, and other data from the Mission to Planet Earth (MTPE) program will be archive at DAACs under the management of ECS. University access to data is provided under the NSF-sponsored UNIDATA service. Finally, I would be remiss if I didn't mention that NASA's Global Change Master Directory (GCMD) which is maintained at the Goddard Space Flight Center at http://gcmd.gsfc.nasa.gov/ has a wealth of information on how to get data related to Climate.
On the subject of "interfaces" to the data, the key is in the conventions for data storage and formatting. Please go to the primary document page, there are many formatting conventions used. Some examples are: BUFR (observational data) and GRIB (Gridded data) are World Meteorological Organization (WMO) standards for data formats (e.g., used at NCEP); EOS-HDF is the data formatting standard for ECS; the Cooperative Ocean/Atmosphere Research Data Service (COARDS) supports conventions for netCDF; the AMIP project at LLNL have put considerable effort into developing libraries for data access, such as products like cdunif/EzGet, LATS, VCS, and DDI.
The GrADS visualization tool (with its own data convention) is commonly used by atmospheric scientists. Vis5D is sometimes used.
In summary: There are three ways of getting data. If the size of the file is O(10 megabytes), or if you live in Australia, then you can use anonymous ftp. If you are want datasets of more than a gigabyte and you're a "professional" then you'll use 10 gigabyte 8mm tapes (some DAACs provide them for free), this is especially usful for gridded or reanalysed data which tends to be "wordy", you might even use tapes for the smaller raw data files (we at the DAO get tapes from NCAR, NCEP for our long term ranalysis observations, while for real time meterological data of the GTS we use anonymous ftp via NCEP). Some organizations (e.g., GEWEX etc.) release temporal or spatially averaged datasets of special use to the community on CD ROMs. These are limited since they're error prone, they're moderately limited in size (regular CDs are 0.5 gigabyte), but they can be easily read on your PC without a fancy tape reader -- but the pros in meteorology/climate research use tape readers and formats like raw IEEE, or metadata oriented formats like HDF, netCDF, COARDS, GrADS, Vis5D, or GRIB for data processing. For visualization they may use these same formats or they may use GrADS or Vis5D formatted files.
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