Like others have already said Civ 6 is a different game, so requires getting used to all the new mechanics. But I do think there is plenty of stuff I have carried over from Civ 5 that is still relevant.
1. Knowledge is power. Spend a lot of time reading the Civ6 wiki, it will give you lots of information/strategy about how mechanics work, leaders/yields/resources/buildings etc. This may seem tedious, but I think knowing how everything works is the first step to really improving your game, link:
https://civilization.fandom.com/wiki/Civilization_VI (notice at bottom of page is Lists/Eras/Concepts/Stats/Misc...a quick way to look up specific things.)
2. Civ is a Snowball game. Small early game advantages are more important than you think. A good example: most players often settle the 1st settler on spawn tile without any thought. Often it can actually make sense to move from initial spawn to take advantage of stronger yield tiles. Sometimes this means settling on top of that lux nearby that gives extra Science/Culture/Faith. Sometimes it means just better tiles around the city. Sometimes you do it because you spot a good place for a sweet district adjacency. But keep in mind that fresh water is your friend
housing is a *****...
3. Plan ahead. You should always be planning out where you are going to be placing new cities and where your districts are going to go. Put pins in the map to remind yourself of this. This is more important in Civ6 because having well placed Districts can have a huge impact on your game. Don't just wait until it's time to place a district and plonk it down where the best current adjacency bonus is. You should be planning ahead of time so you know which tiles you can chop and which tiles to leave alone. I don't excessively chop, but I rarely place a district without chopping whatever is on that tile first. This might seem too difficult, but if you plan ahead, it becomes easier to get that free value. Also if you have planned where a specific district is going to go, and the tile is free, you should always be placing down districts as soon as you have researched the tech and have the required pop requirement in your city. This is because districts get more expensive the further you get through the tech/civic tree, and when you place a district, it locks in the production cost. Once the district is placed, you can go back to building something else if needed, just make sure to lock the district down, before the production cost increases.
3. Lean on Advantages. What advantages does your leader have? What advantages does the map spawn give you? Use the hand you have been dealt to your advantage. Got lots of geothermal fissures/mountain campus spots? Focus on getting the most out of every Campus adjacency, then lean on the 100% campus adjacency policy card. You have the cultural city state Nan Madol near you? Make sure to place as many districts on coastline/lake edges and get Nan Madol Suzerain asap!
4. Policy Cards. Now this is more tricky because it requires a fair amount of learning. However, understanding which policy cards are powerful and which are not makes a big boost to your game. Rationalism comes to mind. The one that gives your builders 2 extra charges is strong. All the 100% adjacency to Campus/Industrial/Theatre/Holy Site are powerful when you set up for it. So largely this is going to depend what overall gameplan you are going for.
5. Timing. Lots of things in Civ require getting the timing right. This kinda ties in with Plan ahead, but anyway... Golden ages can have powerful effects, knowing how many era points you get for doing certain things is important. One thing that
@Victoria mentioned in another thread that helped me was the Governer Amani. An early Amani can be useful to get early Suzerain bonus (which gives you era points). The play is to move her around among City States that you already have 1 envoy in. She will get you Suzerain Era points fast in the early game. This is just one example of timing, but there are lots more things going on... When you are reaching your housing cap, consider popping out a settler so you don't waste food, or just focus on production more so your surplus food isn't wasted. (this is because getting to your housing cap really stunts growth and therefore excess food is wasted when you should be working production instead)
Tbh I could go on for a while, but I'm gonna leave it there for now. I guess the simple answer is, there is no easy way, it just requires a lot of work and studying the game. And to those saying 'spam cities' and 'warmonger and exploit the AI', you can do those things, but I don't think it is the only important deciding factor. I have won games on Deity with only 1 city, obviously 1 city may not be optimal, but I am beginning to think that the optimal 8-12 cities isn't as strong as people think, sometimes fewer stronger cities can be powerful. Especially seen as the deciding factor of Scientific Victories is Production, not only Science. And having a couple of 'Large' 100+ production cities can be very good for completing spaceship parts. Also, you can get some strong games by focusing heavily on Culture output from a couple of well placed Theatre Squares and getting some key early wonders then leaning on the 100% theatre adjacency card, and this doesn't really work if you just spam cities. Btw, I don't ever exploit the AI for money, or abuse stuff like that, I just feel that makes a mockery of the game, and I wish it wasn't as easy to do so. But I don't think it vastly makes my playthroughs inferior. Also, I mainly play to challenge myself and occasionally compete against my friends, and then exploiting isn't really gonna help ;-)
Sorry for the Great Wall of text...