You can require that users fill in certain fields before the user can successfully submit the form. Simply place all field names that you want to be mandatory into this field. If the required fields are not filled in, the user will be notified that information is missing, and a link back to the form they just submitted will be provided.
If you want to require that the user fill in the email and phone fields in your form, so that you can reach them once you have received the mail:
<input type="hidden" name="required" value="email,phone" />