If the Invite User button is greyed out when attempting to add a new user via Setup > Admin > Users, you may not have the required role or privileges.
For example, a user assigned a 'Power User' role does not hold the required privileges to invite users.
The ability to invite new users to the platform is controlled by your user account privileges. You will need to contact your platform account administrator to either be granted the privilege or ask the administrator to invite the user.
For more information regarding roles and permissions, see: Organizations, Users, and Roles