Field api - taking responsibility over a field display
Fields are displayed through formatters (you can have multiple ones, and then you chose which one you want when adding the field to a content type, or any bundle of an entity).
So, hook_field_formatter_info() and hook_field_formatter_view(). 
Open the core image module: modules/image/image.field.inc in your Drupal install, and use that as an example.

You can use hook_field_formatter_info_alter() to add formatters to existing field types (not declared by your mpdule).