Well, it all depends on what you have.

for instance -- if you have SSI (server side includes), you can just do something like:

Another option is to use the whole 'AJAX' concept -- JavaScript to make a call back to the server to ask for a new password, and place it into the field. (of course, then you have a javascript dependancy, and you might as well just do the randomization in JavaScript

Or, there's the bit that's already been suggested, and just have a CGI to spit out the form. I typically go with this approach, and use the same CGI that generates the backend and initial form, so that I can do data validation, and then re-populate the form, marking any problems.

You will have to write a (CGI-)script that dynamically generates the webpage on which is your form. CGI.pm is the archetypical module to do this, but there are many other solutions. Ovid's CGI-course (esp. lesson four and lesson six] will give you a lot of valuable pointers. Personally I tend to use now a templating solution (Template Toolkit) for anything but the most trivial applications, but YMMV.