For those on a genealogy quest, large or small, these are exciting times.

Amateur family sleuths are taking advantage of the vast and growing trove of digitized records on sites like Ancestry.com, FamilyLink.com and Geni.com. More often these days, researchers are turning to social networks for help in discovering connections to the dead, and to the living.

Revelations can be serendipitous, and shockingly fast. Last November, for example, it took Laurel Axelrod just two hours to locate the birth mother of her husband, Nicholas, who was adopted as a toddler. She started with crucial biographical information on Ancestry.com and finished by poking around on Facebook.

Within a week, Nicholas spoke to his birth mother on the phone for more than an hour. “It’s sweet,” Laurel said, “now it’s every weekend.” This spring, the couple, who live in California, flew to England to meet his birth mother and a few other family members in person. “It’s really, really amazing,” she said....