How do polyamory and/or polygamy work?

No judgment, no offense is intended with this question, it’s just something I was pondering while driving around the other day.

Most two-party relationships are pretty straightforward – we agree that we are an exclusive couple, and intimate activities outside that system are frowned upon.

So what are the “rules” of a polyamorous or polygamous relationship? I assume it’s built around a lot of communication and mutual understanding, but… I suppose I’d just like to understand a little better.