To piggy back on the piggyback:
Remember that a new district is unlocked at 4, 7, 10 pop and so on. But keep in mind that you don't need more than 3 or 4 districts in a single city. Specialization is key if you want a fast victory. So, which districts should you build?
General consensus in this forum is that Commercial Hubs or Harbors are the most versatileones, and should be in a majority of cities. Each city with either one of those nets an additional trade route for your empire, and since 2-3 of them can greatly jumpstart a city or boost production, you want many of them.
Next, you should build your "Victory District". Those are the ones your victory will specialize in. So, Campus for Science and Theatre Square for Culture. Encampments have a mixed opinion around here: they give many small boosts, and some consider those justification enough to be built, while others don't, so it's a matter of personal opinion. Usually, you want at least a couple of Campi, but if not going for culture, Theatre Square might be left aside (you can get culture from other sources).
Now, the Holy Site. This is a special snowflake, because 99% of the time you build them (excluding conquered ones), you want a religion. And for that, you need to be fast. It must be the first district you build (and one of the first things you build in the game). Many times, if you're using Religion, then Commercial Hubs might not be so important, because you can buy units and GP with faith using Theocracy.
You also want an Entertainment Complex here and there for amenities. Same for Industrial Zones, though some people like to build those in every city for the production. In my humble opinion, it doesn't pay itself, but a few are needed for Factories and Power Plants.
Aqueducts are mostl important for non-freshwater cities, or as Rome. For other cities, the housing bonus is quite minor for its production cost.
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Now, we chose what to build, where do we build them?
Theoretically, you want them in places that give most adjacencies. But remember that placing a district will override any tile yields. For example, a Plains Hill might give you 3 food and 1 production, but if you place a Holy Site there, it'll only give faith. Also, production is key: a Campus surrounded by 4 mountains may seem nice, but if it's the only place suitable for a Mine, build the Campus elsewhere.
You can turn the yield override to your favor: Building districts on desert or tundra will grant these useless tiles some yields. More importantly, they don't need to be worked by your citizens, so they become productive without diverting your citizens from better tiles.
A good strategy for placing them is making a triangle with 2 districts and your city, since the City Center counts as a district. This way, both districts will get adjacency bonus.
As a rule of thumb: Place districts in flat terrain and/or where they receive most adjacencies. Hills should be mined, and Woods beside rivers should get a Lumbermill (they receive +1 production in those conditions).