When a user signs up and enters their details in your form, you can use the php mail() function to send them an email!
The function is given in detail on the php website:
http://uk2.php.net/function.mail
but essentially it is of the form
mail(string $to, string $from, string $message);
so for example:
mail("
[email protected]", "This is my test email", "Hello world!");
would send an email from your script to
[email protected] containing the message Hello world! under the subject of This is my test email. Simple!
So if you replace the message string with your message (for example "Hello, thank you for signing up. Your username is '$username' and your password is '$password'" where $username and $password are your appropriate variables) then that is what will be sent.