The answer is that by and large they don't have any. The normal MO seems to be find a keen member of staff "who is good with computers", give then a copy of Quark or InDesign, and tell em to go design forms.
They may get a little training on the form design part of the job, but are unlikely to get any and the more subtle aspects of using the software to its full advantage, making it accessible, or even basic stuff like layout, tables, interactive content etc.
Rather like when the IR used to do downloadable PDFs for tax returns - all very pretty in "corporate" design, layout, colours etc. Then they produced a 75 page book on how to fill it out and how to do the calculations needed for all the computed boxes. For an organisation of that scale, how difficult would it have been to make the forms in the document editable, and had the form do all the calculations for you so you could fill it in on the computer, print it and post it? The cost saving in error reduction from not being able to read the handwriting alone would have paid for the extra few days of development in no time!