Query table A for any rows that are like any search term in table B
...
FROM
  TableA
  JOIN
  TableB ON
          TableA.FirstName LIKE '%' + TableB.SearchTerm + '%' OR 
          TableA.LastName LIKE '%' + TableB.SearchTerm + '%'
....


Now, this isn't going to be the best of queries. Consider full text search instead (I'm not too familiar with it)

This OR could be split into a UNION