Maybe somewhat tangential, but for maintaining relationships (close or distant) in general, the best things for me (who am still learning) have been a study of the Bible and Book of Mormon, and some things they said in our church's General Conference, which I will try to roughly quote from memory:

"Never let a task to be accomplished be more important than a person to be loved."

"The primary feeling in any interaction should be love."

"Observe and serve."

This does not mean failure to speak only truth in kindness as appropriate, or to set boundaries when necessary. I think Jesus Christ's example of understanding, truth, and kindness are ideal for us all.

Also as some have hinted here, being a good listener, asking questions, caring about others' background and well-being in general, being humble, willing to share when appropriate, and looking for the good and things to appreciate in others, and ways to serve, can go a long way. Interesting volunteering opportunities (where you would meet people as a side-effect) might be found at https://justserve.org if available in your area.