The thing to be aware of is that the diplomatic game in civ is a cool kids high school club. You're either in the cool kids, or you're in that other group, and that other group is usually that one civ in the corner everyone hates. So, if you try and be friends with everyone, the popular civs are going to say, "Hey, look at that vesp3, he's friends with that guy," and then denounce you. Unfortunately for you, the unpopular civs are then going to start resenting the popular civs and go, "Hey, vesp3's friends with that jerk" and denounce you too. Eventually the rest of the civs in the game will bond over their shared hatred of you, and suddenly you become the one everyone hates, especially if you've done anything else to anger them.
But there's hope! With a bit of diplomatic maneuvering, you, too, can be a cool civ. Civs like it if you hate civs they do. So, early on, choose civs that are going to be your best friend, and choose a civ or two that's going to be your worst enemy. Be very consistent throughout the game. Trade with the civs you like, and share their religion, then denounce the civs you don't like. Bribe the civs you don't like to declare war on the civs you like, then declare war on the civs you don't like right back to get the shared enemy diplo bonus. If you can be active about making both friends and enemies, you can be the leader of the cool kids gang until ideologies come in to play, and if you do it well, nobody will even care about you taking cities from the people you hate, because everyone you care about will hate those civs too.