What can I do to allow my users to sign up and get an email address through my domain? Any help would be appreciated. Thanks.

Well, please mentioned it more clearly that what sort of domain you wanted to have your users have like if you want to have an email address who has domain like someone@yourname.com
so this can be done by on cool hotmail and passport.net if you want this then go for it and if not then mention it clearly.

You need to be running a mail server, for this the cheapest and simplest answer is Linux running Postfix and Dovecot as the mail handlers. You would need to subscribe to a fixed IP address, and set your domain registrar's dns A and MX records to point to your IP. You need to forward the smtp and pop3 ports to your IP on the router. You can offer IMAP web mail this way, but will need to set quotas on user mailboxes. You also need to run a database for user and security control if you need to automate user logins, and must be very careful of mail sending security or your site will become an open spam relay and be blacklisted.