Answer:
When and who you run an OFAC search on it dependent on your own bank's risk assessment. However, it is not FinCEN that provides a search tool, it is OFAC. Using the OFAC search function is pretty straightforward. The websites for the search and FAQs follows:
https://sdnsearch.ofac.treas.gov/
http://www.treasury.gov/resource-center/sanctions/SDN-List/Pages/fuzzy_logic.aspx