1. A user registers at your forum, but with a password to be sent by e-mail.
2. The forum sends him an e-mail with the password.
3. The user receives the letter with the password, comes back to the forum and enters.
What more e-mail validation? If the new user have received the e-mail with the password, obviously he has given a valid e-mail. Of course, everybody could give a valid e-mail address and close it after a while. There is not a medicine discovered for this yet :)
The registration with a password by e-mail is a default feature in miniBB.
Why don't you love reading manuals? :)
Excerpt from the manual:
//$closeRegister=1; It is possible to avoid "open" registrations, when user registers, he enters desired login/password and from the first step becomes a registered user. The $closeRegister variable in setup_options.php now allows to avoid incorrect email address upon registration. If you set it to 1 (default is still 0 or unset), on the registration form user will not see the password field, and will receive it via email (password will be generated automatically). In the user_dataform.html you should have <!--PASSWORD--><!--/PASSWORD--> tags. Upon registration, the content within them will be removed. When user changes data, they will be shown. Having this option set, you SHOULD set $genEmailDisable parameter equal to 0, and $emailusers parameter equal to 1. And of course you should have sendmail working ok.