On September 7, 2017, FamilySearch discontinued its microfilm distribution services. This change is the result of significant progress made in FamilySearch's microfilm digitization efforts and the obsolescence of microfilm technology. Please read the FAQ on their webiste.
Genealogy microfilm from the Family History Library in Salt Lake City can no longer be borrowed. Exisiting holders of microfilm have been given extended due dates. The Family History Geneolgy database is restricted to in library use only.
Start your search here: www.familysearch.org
HOW TO FIND DIGITAL IMAGES ON FAMILYSEARCH
Digital image collections can be accessed today in 3 places on FamilySearch.org, all under Search.
Catalog. Includes a description of all the microfilms and digital images in the FamilySearch collection. This is where all of FamilySearch's digitized microfilm and new digital images from its global camera operations are being published. A camera icon appears in the Catalog adjacent to a microfilm listing when it is available digitally.
Records includes collections that have been indexed by name or published with additional waypoints to help browse the unindexed images.
Books include digital copies of books from the Family History Library and other libraries, including many books that were previously copied to microfilm.
For additional help, see Finding Digital Images of Records on FamilySearch.org, or watch this how-to video "Where are the digitized records on FamilySearch?"