Here are some things I had to learn when moving from monarch to emperor:
City maintenance starts to become a more serious problem. Sometimes simply founding a 2nd or 3rd city can really hit your tech rate and at times it can be good to delay it a few turns while clearing some important techs. Unless of course there is a gold mine or other easily obtainable commerce resource nearby

. The AI will use this tactic as well. Also when I first started on emperor I would always assign the first city pop to work a cottage for every city I would conquer as well as my own. This should help you out until you get better at managing the higher penalties. Alternatively if you are playing a financial civ on the coast, simply building a 2nd city asap and working the 1f/3 c coastal tiles can provide a commerce/science boost as you overcome the maintenance costs immediately.
The happiness caps are a huge problem. You might want to go a bit easier on the whip if you are a big slavery fan. If you have a pop 3 city working 1 farm, 2 mines and you whip once you've just cut your production in half for the next 10-30 turns depending on game speed. Pay close attention to which tiles are being worked.
The city auto governor is generally your enemy. It can be better to turn it off and manually control which tiles are being worked. I check all my cities every few turns to make sure all my peasants are in line with what they are supposed to be doing

. Also when your city grows the governor naturally assigns the new citizen to a particular tile. This can be manipulated by using the emphasize buttons to get the auto assignment to (generally) do what you want in case you forget to check the city immediately after it grows.
City specialization. If you aren't already doing this you need to decide which roles certain cities will play based on the available terrain and then only build those buildings which are appropriate.
Also as discussed diplomacy and tech trading are huge. Beelining certain techs and then back trading the rest is pretty important. For example pulling an Oracle->MC slingshot will pretty much guarantee you will get every other tech you skipped in trade using MC. If you manage to pull a tech lead sometimes you can run 100% science deficit spending nearly the entire game and generate cash by selling your techs.
Running a specialist economy can be a huge early game boost. As was pointed out it only takes 3 pop (the happiness cap) to work 1 improved fish tile and run 2 scientists for 6 beakers/turn or 12 beakers/turn with Representation. Run the caste system system and build a lighthouse and you are looking at 9-18 beakers/turn (sans building bonuses) all for the cost of working 1 tile and a population of only 4. This makes those otherwise useless desert/tundra wastelands mini science gold mines if there is even 1 seafood resource off the coast. You don't even need a library with the cast system, just build the city, improve the food resource and go! In this particular case tile overlap is a non issue as well. It does not matter if I build another city 2 tiles away from the last one to reduce maintenance costs if I only need to work 1 tile to run it.
Cut corners with your workers. Remember that rivers count as a trade network so if your capital is along a river you simply need to build a road from your new city to the closest point on that river to connect them and generate an initial 1c/turn in trade route income. An alternative is to place subsequent cities along the same river if possible, which can delay the immediate need to build a road or even research the wheel tech.
Also discussed was knowing your neighbors. Knowing the different AI personalities and their tendencies is very important. Every time I meet Monty as my neighbor the first thought that goes through my head is 'OK you die first, just give me a minute' following my alt-click for all cities, queue melee units and look around for my copper

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I've also found aggressive queue swapping to be rather important. Actually I would say this made the biggest difference in the game for me. For example, by chopping your settlers and workers you will not only speed up their build times but you will minimize the stunting of your town growth. Build a warrior or archer while chopping and push the settler or worker to the top of the queue when the chop is due. This is hard to beat as you will likely end up with both protective units and settlers completing at the same time and ahead of schedule in addition to growing your city. With a low happiness cap it's absolutely crucial to bring all of your population online as quickly as possible. This is especially true if you are going to make a run for a wonder. When going for a wonder with a cap of 4 in your capital you want to try and shoot for 1 improved food tile and 3 mines if at all possible and adjust your workers and techs accordingly. With AQS you can even start building a wonder while sending your chops to a settler. Very useful to keep from stifling expansion.
Pre-chopping forests can be a huge benefit to give an immediate influx of hammers for a wonder or other important building (ie. a forge to bring an engineer online to generate a GE); however be careful if you are a clear cutter. Watch out for the new health handicaps as they can really ruin your day if you aren't paying attention. Also since the hammer bonus from forests increases over time with the appropriate tech it is sometimes advantageous not to improve every tile if it's not being worked. This will allow the forests to grow back if you didn't clear cut, which can be a nice benefit later.
Pre-improvement of tiles can sometimes be useful. If your worker is busy building a mine with 1 turn left and a barb pops up who will likely pillage it, abort your worker action and send him home until the barb is dealt with. You can then return to the mine and finish it in the same turn, which could save you a lot of precious early worker turns.
I hope that information helps. Welcome to the Emperor club

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