You can access Mormon ancestry records on the website FamilySearch.org, a website operated by the Mormon Church of the Latter-Day Saints. While there are other genealogy websites and resources to trace family history, this website is the most comprehensive for those with Mormon lineage.
To get started researching Mormon family history on FamilySearch.org, simply choose the search option centered at the top of the Web page. You do have the option of signing up for an account to receive emails and assistance from the site, but it is not necessary to begin your search.
It is important to note that the Church of the Latter-Day Saints and the site FamilySearch.org represent the largest genealogical library in the world and part of their mission includes encouraging the over 15 million Mormons to research their family history. Many Mormons feel it is their religious duty to track down their ancestors in order to perform temple ordinances and secure their eternal life. It is part of the fundamental Mormon belief that family is eternal and not ended with death.
On the site you can search for individual records, genealogies of others, and even build a family tree with portraits as you move along. There is also an option to volunteer for the site to help other people research their history.