Occasionally,  when I click on a site to download a program, my Firefox browser closes unexpectedly.  If I want to download a particular program, I must then open Internet Explorer and then I do not have a problem downloading.  What must I do in Firefox to enable me to download programs?

   It is so tempting for me to say just ditch Firefox and use Internet Explorer especially since some people have ridiculed me for not switching to Firefox, but I won't say anything.  :)
   Since I don't use Firefox, I don't know an answer to your problem.  Maybe someone else will.

I understand that your FF does not *always* close unexpectedly. There can be a lot of reasons, so I cannot give a general answer. Mozilla knowledge base says for instance: clear up the download history (open with Ctrl + J).

With Windows I use FF, Opera, MSIE, and mostly follow that order if a download will not start. I will also look what the particular site actually does when you click "Download". If it switches to a different domain, FF can be a lot more "picky" about redirection.
However, in that case FF does not hang or crash, but just stops (mostly).

Personally I think it is a good thing that my browser is a bit particular about who its friends are.
But then I hardly ever have trouble with downloading via FF.