It's not something that is really possible to do from Instant Web Publishing. Closest option I can think of is that you add a table where the users fill in a "request form" where they specify their email address and the criteria identifying the data they want to export. Then a script from the host computer, one performed on a regular schedule (every day, every hour? or ???) set up on the host machine uses the data entered in this "request" table to find the records and then emails a tab, csv or excel file as an attachment to the person requesting the data.
Note that this takes quite a bit of design work and scripting to pull off.
How you schedule such a script to run on regular intervals will depend on whether you host your databas with FileMaker Server Advanced or just FileMaker Pro.
Export the data on a daily (hourly) basis to a location available to users? SImple and sorta foolish proof.
If there is no need to export user specific records.