How do you theme specific fields in on a content type? Currently I want to theme a taxonomy field in my content type and expose the TID and the Term name with link. The default sections only give me one or the other. Is there a setup where I can expose the TID, Term name, and Link? 

Below is a screenshot of the teaser view display mode.
You could use field.tpl.php

If your field is called field_series then you will need to create:

/mytheme/anyfolder(optional)/field--field-series.tpl.php

If you inspect the variable $element then it will contain everything you'll need (tid, name, see drupal_get_path_alias for the link)

Don't forget to clear the cache once the new template has been created.