they/them pronouns

I just saw a very beautifully spoken video about a person's journey being bi-gender. And as I saw the thousands of hateful comments of how they dont care and it shouldn't be shoved in their face, it was easy to realize they missed the point entirely. And as I wanted to comment, I hesitated because I don't know exactly how to use they/them pronouns (and didn't want to use he or she). is it "they" when you would use words like he or she, and then "them" when you would use words like him or her? I don't want to be insulting or anything.