Civilization – Green lights in ocean

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).

There are many reasons to go to war with another Civ:

• Take their territory and resources - although the game is more balanced towards making small Civs profitable than ever before, in most cases having more territory/cities/resources can still give you a big advantage.
• Halt the progress of another Civ who is doing better than you in some other area - if you have the military, you can stop a Civ who is doing better in technology or culture but who is weak militarily.
• Defending allies or forging new alliances - war is a powerful way to increase your reputation with allied civilizations. Allies can make war against you more difficult, and they'll be more receptive to trade agreements that are beneficial towards you.
• Nip a potential adversary in the bud - the AI in particular is terrible about unit tactics, so you may be able to provoke them to attack you and devote resources to war before they're completely ready.

Depending on why you're going to war, your goals/result will differ. You may wish to simply weaken their army, force them to give you money or other resources, or take a strategic city, but if you're going for a Domination victory, you're going to want to capture or destroy all of their cities, despite their (likely) pleas for peace.

Be wary of growing too large too quickly, as happiness is critical to growth, and extended war and capturing cities leads to rampant unhappiness. If you devote too much of your Civ's resources towards building and maintaining an army, you may fall behind in other areas, giving others room to outpace you.

I tend to prefer to puppet captured cities (instead of razing or annexing them) as this tends to provide a pretty good balance between the benefits of having more territory, resources, and population and the detriment of unhappiness due to size. There may be cities that are just worthless (ie, population 1 or 2 cities in poor positions) and need to be razed, or cities that are extra valuable (ie, high population cities with wonders or other beneficial buildings) that you'll want to keep tighter control over.

Unit tactics have also changed significantly since Civ4 - in that game, you wanted to build large stacks of units to march across enemy territory with at least moderate losses. In Civ5, if you focus on a few powerful front-line defensive units coupled with ranged attacks from siege units, you'll find that your investment in units is small compared to enemy losses. Siege units in border cities can make mincemeat of overzealous enemy armies once war is declared.