1. Register an organization in your database with their name and domain name. Check the end part of an e-mail to see if it is the same as the email given in your registration form, below using php -
$email_parts = explode('@', $email);
$email_domain = end($email_parts);
2. When setting up the organization, create an admin password that a user must submit before they can register. Compare the password entered to the given one, if it fails, they cannot register. (not best or secure way though)
3. Have an admin at the organization to enter a new user to your database. If they do not exist, they cannot register.
4. More advanced, get the I.P. address from where they want to register. This might however not be very reliable as some people might not be at the office or on the same network, this will then ultimately fail registration.
These are the ones that popped to mind, hope it helps.