Add data from one table to another when data in two other specific fields are identical
You could try an UPDATE with a FROM clause, from your description of the problem.

Something like:

UPDATE table1 t1
SET new_field_for_fk = t2.pk 
FROM table2 t2 
WHERE t1.county_name = t2.county_name 
  AND t1.farm_name = t2.farm_name ;


Should update all rows based on the matching of the two keys across the tables.