The simplest is to use a script that opens a custom dialog with an input field in it for entering the password. The input field has a "password" option that replaces the user's input with bullet characters.
You can "roll your own" by either formatting a text field with a "dingbat" font--but it looks less professional or by installing a "bullet font" and using it to format your field.
You can also use Manage | Security settings to make the fields view only with a script that uses Relogin to re-open FileMaker's password dialog. This can replicate the "manager approval" process that you see many cashiers go through when their software stops them from doing something until their manager comes, approves what they want to do by entering their manager password to approve it.