How do I add additional tabs for the contact?

Additional tabs for a contact contain custom fields. To create custom fields, go to the Administer CiviCRM menu. Click on Custom Data, under Configure.

When you create a new custom field group, in Settings make sure to choose the Display Style as Tab. All the custom fields in this group will now show up as a new tab in the contact record.

For more information, see Custom Data Fields & Custom Data Groups Admin.