There's a lot to write about, so to give this some structure I will use the scoring categories as starting points.
Number of cities and city placement
You want to settle as many cities as you can, of course. Growing two cities to pop 30 requires less food than growing one city to pop 60, and you get twice the local happiness to do it, as well as extra food from a second Granary, Hospital etc.
Cities must be at least 3 tiles away from each other (2 tiles if on separate landmasses), so your settling pattern will be dictated by the terrain and the placement of CSs and AI capitals. One little trick is to include Venice as an opponent, because you can raze CSs that have been bought by Enrico. Austria would work too, but the AI is incapable of diplomatic marriage on Prince. As a side note, some other good AIs to include are those that can found a religion quickly (Ethiopia and the Celts; not the Mayans because they like Oracle too much and don't ever build their UB anyway), and those with UIs that provide extra food (Netherlands, Morocco, Inca).
In this gauntlet I would take screenshots of my starting area when I got Collective Rule, and figure out my city spots. I rerolled maps with really unfortunate CS/AI placement before committing too much time to the game.
If you have two alternative spots where you can place a given city, pick the one that generates more happiness and/or food. Some examples:
- Farms are +2 food while Pastures and Plantations are +1, so settling on plains/grass Cattle loses 1 food, while settling on flat plains/grass loses 2 food
- Settling on flat land unlocks the Windmill, which gives you +1 food and +0.5 happiness with Freedom
- Settling on any tile will turn it into a 2-food tile. You can use this to maximize the food available to you by settling on hill mining luxuries or snow
Population
A 27-pop city generates 3 global and 27 local unhappiness. With Forbidden Palace and Meritocracy this becomes 3 global and 22.95 local unhappiness. Global is countered by +2 happiness from Aristocracy and +1 from Meritocracy. Now we only have 22.95 local unhappiness to worry about. Happiness sources available in every city are:
+6 Colosseum/Zoo/Stadium
+2 Pagoda
+2 Religious Center
+1 Goddess of Love
+0.5 Ceremonial Burial
+2 Bank and Stock Exchange (Capitalism)
+5.5 from 11 specialists (Universal Suffrage, assumes Factory but not Windmill)
+2 from Hospital + Medical lab (Urbanization)
+1 from Castle (Neuschwanstein)
+1 from city garrison (Military Caste)
= 23 happiness.
Which means that a 27-pop city is completely self-sufficient, you don't need to spend any of your global happiness reserves to support it. So you want every city on the map to grow to pop 27 at least. Since that's really close to 30 pop which gives another +1 happiness with Aristocracy, my rule of thumb is that every city should grow to pop 30. Many of them will have extra sources of happiness anyway, such as Windmills, Watermills, Circuses etc.
So in this game I tried to make sure that all of my cities had enough food to grow to pop 30. For this you need at least 48-54 raw food per city: 9-12 food for 9-12 specialists and 36-42 food for 18-21 other citizens. So after settling all the cities and capturing the CSs, I spent some time assigning the tiles to make sure that even the worst cities had enough food to grow. A few of them needed caravans.
As I mentioned before, my religion in this game was Goddess of Love, Ceremonial Burial, Religious Center, Feed the World and Messiah. William had a religion with Desert Folklore and Pagodas, Haile had Stone Circles, Mosques and Cathedrals. I took Amsterdam very quickly, but when Haile founded his religion with Mosques, I knew I had to give him time to enhance. The Celts had taken Monasteries, so I knew there was a good chance Haile would enhance with Cathedrals. If you're trying to take control of two AI religions, letting one of them enhance also helps because it gives you access to Inquisitors.
My endgame routine starts on turn 300. I let happiness go down to 0, schedule as many cities as possible to grow on turn 324 or so by juggling tiles around again, avoid growth everywhere, then let every city grow and go very unhappy, then build CN Tower to get another pop everywhere. Archaeologists start digging out artefacts, since I don't need farms for growth anymore. GWAMs create great works.
In the early game I kept most of my cities except the capital around 6-pop and let them build Settlers and Workers, while the capital spammed wonders. When Zoos became available, I grew my cities to pop 10-12. Forbidden Palace gets built around that time as well, which helps a lot. The next big jumps in population come at ideologies.
Wonders
This is pretty straightforward - you want every wonder in the game. This includes International Space Station and all three ideological wonders.
In this gauntlet I didn't compete with the AIs for the Great Library and instead went for Stonehenge first. It gets you a religion reasonably fast even without a faith pantheon. After that I would pretty much beeline Guilds, and build ToA, HG and Petra. This way you get your first natural Great Engineer around the time you research Guilds. Machu Picchu is a good wonder to rush, especially if you don't have a mountain in the capital. Extra gold from city connections helps a lot and the faith isn't bad either.
You can let the AIs build some wonders for you. Just make sure you get Oracle for the free policy, and keep an eye on the AI that you plan to leave alive, so that they don't steal any wonders from you. You probably want to get Great Wall quite early, because it's doesn't have a "skeleton" in the city where it's being built.
For ideologies, I like to go Autocracy first to get double strategics and build as many Factories as possible. Engineer-rush Prora, propose WI: Order and switch ideology. Build Kremlin, repeal WI: Order, propose WI: Freedom, switch ideology again. You'll likely get a turn rollover with massive unhappiness when you switch, so rebels can spawn. Make sure you're prepared to deal with them.
Tech
Future techs are worth 10 points, so you'll want lots of Great Scientists in the late game. For this reason I like to propose Science Funding as my second congress proposal after Culture Heritage Sites. Then you want to research Radio before the third congress session for either World Ideology or International Games.
You can't really convert Great Engineers or Great Merchants into victory points, so Great Scientists are what you're after. The first GSEM specialist slots you should be working are University slots. This will make sure that the first Great Person to come out of the city will be a Scientist.
Policies
My early policy path was Tradition opener -> Collective Rule -> Piety to +1 faith and cheaper buildings -> finish Liberty -> Aristocracy and Patronage (Forbidden Palace) for the 10-pop city spam. Piety is crucial if you're planning to control an AI religion - you'll need lots of faith to buy missionaries and buildings.
In the long run you simply want all the policies that give you extra happiness, food, great people, great works and access to wonders. To the Glory of God is a good reformation belief to get, as you'll need GWAMs for great works and maybe Great Generals to steal land from the poor AI you've left alive.