In order to add an A330 type rating to your FAA ATP you would have to complete a ground school and pass a type rating checkride. You would then be authorized to act as PIC on a 330 under FAA rules.
The FAA SIC type rating was created so foreign CAAs would know the pilot had completed SIC training without the pilot having to carry their training records with them. To add a SIC type rating to your FAA certificate, you would training records stating that you completed SIC training within the last 12 months and an endorsement in those records that states that you have "demonstrated the skill and knowledge required for the safe operation of an A330, relevant to the duties and responibilities of a second in command." Fill out the application and bring it all to a FAA office or a FAA designee.