Here's an order of things I do in my culture games, which give results:
1. Settle as usual, kick out 3-4 cities, use the NC start as you would in a Science game, because Science is believe it or not, more important. However...
2. ...try to get Oracle, one free policy early on is VERY good. It could even allow you to switch between Tradition and Liberty and get the best of both worlds. In my opinion, a free GE as a Liberty finisher trumps Tradition finisher in the early going. Aesthetics opener is nice for after you got your Guilds up, it works well with Gardens and National Epic, all of which should be available before you...
3. ... beeline to Education, as you normally would. Get Unis up and fill the specialist slots. Plant 2 GSs, save the rest for later. Your cities should be at least pop 10. Keep them growing because more often than not...
(At any point, if opportunity presents itself for you to found a religion, do it. If you're Ethiopia or Celts, definitely do it. Watch out for warmongers, pay them off to go stab someone else. But use composite bows to defend. Religion is *not* essential, but helpful. If you go for a religion, opening Piety is a good advice. But don't finish that tree just yet.)
4. ...there are two options to go from here, and it depends on the state of other players tbh: You either punch into Renaissance, get Sistine Chapel (with the saved GE if needed) and open Rationalism for more beakers, OR swing back down the tech tree and grab Pisa for a boost of GPP and (hopefully) one more GE. Sometimes you will have enough time to do both.
5. Stop! Are you happy? Why not? You should aim to be really happy at this point, double digits happy...
6. ... because there's no point in going further Aesthetics when you're not really happy. A free Golden Age isn't really important in general at this point either...
7. Time to go Freedom, which means more great people points, less food needed to feed them and ultimately more happiness. Do you have Hermitage? You should by now. You could also use either or more of the following: Louvre, Sistine Chapel, Uffizi, Globe Theater
8. Do you have Archeologists running across the map. Museums? That's good, the more the better. Remember, if your cities can reach it, Landmark. Otherwise, Artifact. Show respect for the cultural heritage of other nations. By not ninja-ing ALL of the artifacts
9. Landmarks plenty, theming bonuses online. Time to finish Aesthetics and get to Freedom lvl3, and get Hotels up everywhere. Oxford? Yeah it should be quick now, get it, fill it with two great works of writing, thank them for the free tech (Radio).
10. If you didn't burn the GEs, use them now if you want, one for Eiffel Tower, other for Statue of Liberty later on. If I remember correctly, that's all of the wonders you essentially need.
11. Saved up enough GSs? Good, use all of them to get Internet. In the meantime, build National Visitors Center, and finally start making great musicians.
As a rule of thumb, get Open Borders from everyone, don't allow Open Borders to anyone. It could be considered an illogical hax but it's for the best.
12. By this time, most of the map should be under your influence. Open Borders from everyone and shared trade routes all add up nicely. Diplomatic propaganda is unlikely if you played well, because if you went Freedom first, everyone else will be forced to go Freedom for the sake of public opinion. Which you control.
13. The ones that are a bit more ahead, use Great Musicians. If you got any Great Musicians before all of this, well, you'd be wiser to get more great works from them. Otherwise, if they popped after the Internet/National Center they're more likely to do really good.
Some more notes: Arts Funding is generally well accepted as a resolution, you *should* delay Cultural Heritage Sites because most of the early game wonders belong to someone else and Historical Monuments are also a good thing to have if you have Landmarks and Academies around (and Holy Sites). World Fair is something you *can* do without, i.e. you'd be better off if it never happens because more important than you winning it is that SOMEONE ELSE DOESN'T. Otherwise, you'd have a culture runaway and those are bad news. International Games, yeah why not, you generally have a good shot at winning that, but more often that not, that is proposed too late to be really important.
I think that about covers it