What is the best way to learn a new game?
I think the best way to learn anything is to actually do it. Reading the rules and watching play are great, and they’re an important part of figuring anything out, but I think the best way to learn a game is to play it. That way you understand what parts of it work or don’t work for you, you can ask questions about the parts you don’t understand, you see where you have fun, and over time you refine it all into an accurate opinion of the game. It’s even better if you can work with somebody who already knows what they’re doing, but you’ll still get a better picture of the system by slogging through it together than you would from watching those people do it without you.
I do need to point out that no matter how you learn a game, you won’t get anything if you don’t want to learn it. It’s the difference between watching video game speed runs because they’re fun and watching them because you want to learn and duplicate the tricks. If you just want to play a short campaign and never touch the system again, that’s fine, but if you’re going to spend ten years in D&D you may want to remember that a full attack action requires a full round. It’s in the name.