To achieve this verification process, you have to set up a PHP site logic which allows you to enter your credentials, then generate a confirmation hash, create a link such as http://www.yoursite.com/activate.php?user=xxx&hash=1a2b3c4d5e and send it along with the email (SMTP). You also set a variable (e.g. bool/tinyint "active") to 0 so the user can't log in until he activated the account. You'll also need kind of a database to store the credentials and hashes and other parameters.
On the other hand you have to build a "activate.php". When the user receives the email, he should have a link which contains username and hash and redirects to the activation site. The site $_GETs the parameters (here named user and hash) and fills them into a textbox each. Then the user has to click on "activate", "active" gets set to 1. Then the user is able to log in.
There are dozens of tutorials on youtube, just search there.
Examples: https://www.youtube.com/watch?v=ngqeWUIDlnk or https://www.youtube.com/watch?v=A9jiyJ5tRBU