How do I create an invoice?

My form is at https://form.jotform.us/DLAForms/conference-information--registratio

Our form is a conference registration form and we are collecting registration fees for the conference.

If a person selects "Check" as a payment option, how do I create an invoice that they'll receive with their email confirmation message.

You could send the user an email autoresponder, you could also format such email as you want and include the needed information. 

This guide will help you adding the email autoresponder to your form: https://www.jotform.com/help/26-Setting-Up-an-Autoresponder-Email 

Let us know if you have any question, we will be glad to help.