I'm creating a website which allows others to create their own email address. Obviously I'm using Roundcube. How do I set-up a page for people to register for their own email address?
Roundcube is only a remote IMAP client, not the email server. Account creation will have to happen within the back-end mail server, not the IMAP client. How to set this up will depend on what you are using as the email back-end.
Once the account has been created in the back-end, only then can a user login to it via Roundcube (or any IMAP client, for that matter).
Ok. Are there any tutorials on how I do this?
Probably. But you'll need to search for a tutorial for whatever back-end email server that you use. Such as Hmail, sendmail, Postfix, etc. Nothing like that will exist here.
If you use a mysql database to save the user mail accounts, you can very simple program a Little script, the insert a new user entry.
Use PHP and PDO.