Yeah, there's some good tutorials out there detailing the basics. The main key is that, generally speaking, you're racing against the next biggest culture threat. So whatever you "need" to win you notice is what the second place civ "has". So needing 576 tourism is a lot, so I expect there's another civ out there who also has a ton of tourism. One strategy is to simply remove them from the game. So, for example, if you have 80 tourists in their civ, by wiping them out you would lose those 80 tourists on the counter, so you'd be down to 463. But if the next highest civ in culture is only at 420, then you'll win because you're already above that.
The other point is to pay attention to some of the multipliers. Sure, grabbing more great works is nice, but sometimes a single trade route to a civ can give you +50% or more depending on great people and policy cards, which can have a massive impact.