Civilization – How to work towards being able to friend an AI

The answer is: it depends. :)

The best strategy is to have a strategy, i.e. decide how you want to win the game in advance. Are you going for a domination victory? Scientific victory? Cultural victory?
Pair this with your chosen civilization and the surroundings of your city(ies) to decide what to build and research.

Are you going for a cultural victory and are playing Ramesses? You should try to build as many wonders as possible and any improvements that'll help you do so.
If you're going for a domination victory with the Chinese though, you should go for military buildings, anything that'll enhance production of great generals and happiness-boosting buildings (since your sprawling empire needs to be kept happy).

For any civilization though you need to balance these decisions with the given situation. Is your city in the mountains but has very little access to food? Then you can safely skip the production-boosting buildings but should concentrate on granaries and water mills. Or are you situated on a tiny island? Then harbors and marine buildings should probably be your preference.

You need to play to your civilization's strengths and balance out your situation's weaknesses. Playing "evenly all over the map" usually works in easier difficulty settings, but you'll need to specialize and focus on higher difficulties. If you set yourself a goal, the question of what to build or research next usually answers itself.

Try to shoot for a cultural victory for instance, and begin by choosing an appropriate civilization. This should be a good experience to show you how playing a focused game can turn out. Playing "all random" is usually more challenging, since it may take quite a few turns until you have formulated a strategy (or you may never get around to formulating one at all).

Anecdote: I just won a cultural victory with the Egyptians, and it was an enormously fun game. I had all of two cities with no military power to speak of (two Infantry units rather late in the game). My empire was tweaked to perfection though and was oozing culture (obviously) and money, which I used to keep good relations to my neighbor Wu (China), who apparently went for a domination victory. I was declared war upon twice by other civilizations (once by two civilizations teaming up against me), and both times used my good relations to have my enemies wiped out by China for me. I had to bribe my way through the last 20 or so turns, since Wu and I were the only civilizations left (~40+ cities vs. 2), and I was the only thing standing in the way of Chinese world domination.

Lots of interesting gameplay to be had in this game. :)

Notice there's a difference between improving a tile and working a tile. Usually you will improve tiles around your cities and then send citizens to work these tiles, but this connection is not necessary.

Improving a tile

To improve a tile, you need it to be within your cultural borders (the tinted area) and reachable by a worker/work boat, and you need to have the appropriate technology. Once a tile is improved by the worker, you get any luxury or strategic resource on it, but that doesn't mean you get the tile benefits (e.g. +production, the small hammers) - you have to work a tile for that.

Pay attention: cultural borders can reach practically everywhere, since cities can expand these borders up to 5 tiles and great artists can expand it arbitrarily further. I once used 3 great artists to reach a far away tile (Aluminum...), it takes time because there's a cooldown between cultural bombs, but it's doable. "Culture bomb" is the name of the great artist's ability which does it. However, in practical terms, if you want access to any resource the best way is to build a city up to 3 tiles from it. Usually when I build a new city I only consider things in radius 3 to be interesting, anything beyond it just usually takes a lot of turns to get.

Notice that some worker actions, such as cutting down a forest or building a road, do not require the tile to be within your cultural borders.

Finally, if you build a city directly on a tile it doesn't count as improving the tile (the tile benefits won't change) but you do get whatever resource is on it.

And as Raven mentioned, to improve tiles at sea you must construct a work boat from a coastal city. Unlike workers, work boats are consumed when they construct an improvement, but they are otherwise very cheap.

Working a tile

To work a tile, you need it to be within 3 tiles of one of your cities, and then that city gets the benefits listed on the tile. In your screenshot, Krakatoa is unworkable, and no civilization will never get the benefits listed on the tile. Notice that even tiles in range 3 are not automatically worked, a citizen must be allocated to it. You can manually allocate citizens from the city screen but the computer takes care of it by itself, if you're new to the game you don't need to worry about it at this stage.

Your puppet cities also send their citizens to work nearby tiles, but you cannot change that allocation.

A tile doesn't need to be improved in order to work it, but most tiles benefit from improvement so ultimately it pays to improve any tile within range 3 of a city. Improving a tile beyond range 3 which doesn't have a resource on it offers no benefits (unless you improve it to a fort or something).