There is more on validating form fields at
http://www.gmayor.com/formfieldmacros.htm however you cannot force users to run the macros.
As you are using macros anyway then it might make more sense to provide a userform to collect the data, write it to the document and to submit the form by e-mail. That way you can more easily check whether the required fields have been filled.
The alternative is to add code to the submit button to validate each of the required fields before allowing the process to complete.