When I'm explaining game rules to someone new, my goal is to teach them without overwhelming them with irrelevant info, and without boring them into zoning out.

I've found the most important thing to be the order in which I present information, and the best approach to be layered, like an onion. Essentially, I give them a broad overview of everything, then I do it again but with more specifics, then again with even more specifics, etc. Each layer provides context that will make it possible/easy to understand the specific details that I'll be explaining in the next layer.

This runs counter to how most people and rulebooks explain the rules. Usually they try to group related facts together, e.g. "Here's all the rules for movement," "Here are all the rules for scoring," etc. That's great as a reference for people who are trying to look stuff up. But it's horrible for a beginner, because (as the linked PDF explains) it ignores cognitive load. It gives people information that only makes sense in context, but it doesn't give them that context, so they don't understand it. So they're forced to say, "Fine, I don't understand these details yet, but I'll just hold them in my short-term memory while I continue to read the rules until I get some context that helps me understand." But our short-term memories can only hold a few items, and they usually start to overflow pretty fast, long before the rules add the missing context we're hoping for.

It's the equivalent of telling someone, "Hey, remember this number: 1823. And remember this number: 9094. Don't worry, I'll tell you later why you need them. But first, remember 6642, too. And 11456. Got it? Okay, just a few more things…"

Ugh.

Here's how I explain stuff instead:

1. Start with the goal/objective. For example, "The goal is to be the first to get to 10 points." The goal is the most important context there is! Without it, people have no idea why they should do anything you explain, which means they won't fully understand anything you explain, because "why" is one of the most important parts of understanding.

2. Explain the general flow of the game in simplified terms, and connect it to the goal. For example, "It's a free-for-all, not a team game, so you're trying to get to 10 points by yourself. We're going to go around in circles where we each get a turn. On your turn you'll take some actions that try to help you score points, or at least set yourself up to get closer to scoring points. Then once you decide you've done everything you can, you end your turn, and it moves clockwise to the next person."

3. Discuss the mechanics of how to win, i.e. how to accomplish the goal. For example, "So how do you get to 10 points? Mostly, you can build buildings in this game that are each worth points, usually 1 or 2 points. So the most basic way to win is to gather resources and build lots of buildings. But usually that's not enough to get you all the way to 10 points. So in addition to buildings, there are a few special bonuses and cards you get can get that can also give you 1 or 2 points and push you over the edge to 10 points. I'll explain those later."

By now, the players have heard the goal of the game repeated three times, they understand the basic flow, and all they've even been vaguely introduced to some strategies, details, and mechanics. With each step, they have more high-level context that makes the specifics I reveal later much easier to understand. (By the way, the game I'm explaining in this example is Catan.)

4. Keep explaining things recursively. Always explain a goal/strategy, so people know why they're acting, before you explain the mechanics of how to do that action.

This has always worked fairly well for me. It's essentially just respecting the "curse of knowledge," which you do by accepting the implications of the fact that your listeners don't know what you know.