Filter results using taxonomy terms
IMHO the best way is to add the taxonomy's name to the index.  This may not be shown as an option in D7 if you have not asked for the fields to be extended to the referenced entities.  

Note: expanding the field list in D7 can make the field list take Minutes to load and you may get a few script running long warnings.  Be patient and let the script keep running.  The list will come up eventually.

Once you have the text in the index, you can use this in either the search view filter or use it in a facet.

An alternative would be to add a relationship between your term id search field to the actual term data.  Then you should have the term name available for use.

Note that this method will add a lot more overhead to your search than just having the term names in the index.