Andres Gonzalez, 19, stands on the balcony of his Los Angeles apartment, his hands in his suit pockets. It is his first week as a missionary, but today, instead of approaching people on the street, he is shooting a video that he will later post to social media.

After about a dozen takes, he is successful. “Hello! If you would like to learn more about Jesus Christ,” he says to the camera in Spanish, “contact me.”

Mr. Gonzalez is the image of the modern missionary for the Church of Jesus Christ of Latter-day Saints, which has changed many of its practices — from how missionaries preach to how they dress.

The faith, long known for sending tens of thousands of neatly and formally dressed young people across the globe each year to preach door to door, is encouraging new missionaries to spread the gospel on social media and, for some, with acts of community service closer to home.

As a church leader, Dieter F. Uchtdorf, put it, missionaries should feel comfortable sharing their faith in “normal and natural ways.”

In the last few years, the church has also changed some rules for missionaries themselves — loosening restrictions on dress codes (women can wear pants) and how often they can call family members back home (once a week, not just on Christmas and Mother’s Day).