One way is to have a small frame (or iframe, probably) that you post to that pops up a javascript prompt similar to what b10m suggested. This can be annoying.

Another way is to have javascript open a new window (window.open) that calls out to your perl script which displays the html for a prompt and talks to the parent via javascript. Can also be annoying, but in general I have used it without real problems.

Yet another way (probably) is to use dhtml to pop up something. I have only played with dhtml a little, but I am guessing you should be able to build a prompt window that is hidden, and have it pop up and do its thing when you click the right button.

All of these use javascript to some level, usually what I will do is us javascript to copy whatever they type in back to a hidden form field, then submit the form... not overly difficult.