Anybody can register a new account at a Gramps Web instance, but it will need to be enabled manually by a site owner before it can be used to log in.
Submit registration form
The home page of Gramps Web, showing the login form, has a link "Register new account". Clicking on it will show a registration form with four mandatory fields: username, password, e-mail address, and full name. When all four fields have been filled, click "submit" to start the registration process.
Confirm e-mail address
After the form has been submitted, an automated e-mail will be sent to the e-mail address provided containing an e-mail confirmation link. Clicking it will open a confirmation page.
If the confirmation e-mail does not arrive (and you have checked your Spam folder), it could be that e-mail has not been configured correctly by the Gramps Web server administrator.
After the e-mail address has been confirmed, the Gramps Web administrator will receive an e-mail notification and can enable the new user account by going to the "User administration" section in settings page (accessible via the user icon in the top app bar) and changing the user role from "disabled" to any of the other roles.
Note that the new user will not receive an automated notification that their account has been enabled, so it is advisible for the administrator to notify them personally.