WELCOME TO THE FORUM!!
(this really is the best place for info)
I've taken a look and will try to explain some things which are important for your empire.
I know nothing of Civ5 (only that it's the sequel to 4), so I don't know what habits you picked up there, and that doesn't matter anyway.
Aaaaah hoo!
(this might be lengthly, but hey, who cares right.)
First of all: Cities!
Civilization is a game of taking control of the World you're given. You have a nice continent, although the capital is placed quite away from the center, there are some basic improvements you can do.
You should see a city as a place from where you work the land. So Tenochtitlan, at size 12, works 12 tiles at the moment (12 + city center)
So the idea is to build cities, and 'work' all the tiles on the continent first, and expand from there.
You've laid down a nice framework of cities, but you really need more cities, and
then large cities.
Just pump out settlers and workers until the whole continent is settled and improved. In the picture below you can see where there's room for more cities.
The black squares give a rough estimation of how I would place my cities on your continent.
Other than near Tenochtitlan, there's no fresh water (river/lake) on the continent so the cities won't grow past 6 people without aquaducts. So they can be place close together.
From here you can make workers, improve the tiles and build you economy, industry and science.
Those are not sink holes, sir.
Brings me to 2: Roads!
Roads. Where we're going, we will NEED roads.
Roads are your friend -> Friends are good -> Roads are good.
Roads do a couple of things, besides just laying there.
1: Roads connect cities, so they...
A: make it easier to walk from town to town with a unit. On roads, you can walk 3 times as fast and...
B: connect cities to share resources. Resources are hose nifty little things that make your people happy (luxuries, lux) and do other things like Iron and Horses which allows for Swordsmen and Horse-units.
Atzcapotzalco (in the South) is not connected, they don't enjoy Silks. Which is too bad.
Also, if you connect more than 1 resource to the Capital then you can trade it, if the capital has a trade network (of roads, or in this case harbors) with another Civ! Whoo hoo!
2: roads give you more commerce for every worked tile. If you lay down a road, a worked tile will give you one extra commerce.
More commerce = more money to be divided into science or the treasury chest.
Which always brings us to 3: Workers.
Half jokingly I've read here that:
the rule of thumb about workers is that you never have enough workers.
Workers are your friend -> friends are good -> workers are good.
(if friends are not good, they are not a friend)
You know that you need to improve the tiles (roads add commerce, mines add shields, irrigation adds food), so we need to make a bunch of workers to do it with.
You're better off with a developed country and missed a Wonder or 2 than with all the Wonders in the World, but vulnerable for attacks, because your infrastructure is neglected.
In the pic below, you see that for those 5 tiles, you could have added 5 gold per turn (GPT) and 5 shields per turn (if those tiles had a road and a mine).
And lastly 4, a bit of empire management.
You're in a Monarchy (good) and have build some wonder to keep the people happy (good), but you've built City Walls in Tlacopan, to defend you against... who? You don't need all improvements.
You could have built another unit with those shields.
I would build a worker in Tlacopan, build irrigation towards the city, make the city grow with more food and then go from there.
In the black boxes in the picture below, you see that you don't need the Luxury slider to keep the people happy, so you may set it to 0%. Then I always slide the Science slider to the smallest tick that at least makes me
some money so I always run a little profit for when I need it. And to have the fastest science.
When I notice that I only need 4 more turns, I slide it back a tick and see if it still says 4 turns. If it does, I keep it there. I also do that when there's 3, 2 and 1 turn left is to the next Tech.
So in the end it's a matter of priorities.
City improvements and Wonders are not important to start a game, working land is.
So build Settlers and Workers (more than 1 Worker per city) until we can't expand no more, then worry about the rest.
Oh and PS, one last thing.
Don't automate your workers. The use of workers is one of the biggest advantages we have over the AI, so don't let the AI do it.
Here's some preferences which gives you some better control over the game (just hit CTR+P in the game and it brings you here.)
Important is the 'ask for what to do' stuff