After many years of lonely searching, my caravels find something in the fog:
Looks like an unoccupied island; the only settlement I've seen is a barb one. I hope to be able to build some colonies here a little bit down the road. With a Forbidden Palace, the mainteance costs wouldn't even be that bad...
More exploration, as I find America on the next turn, just a little bit to my west.
FDR is the leader of the Americans. Their island is quite large, but naturally they're quite backwards in technology. I trade for the world map, and see that FDR has no religion?! Time to run some Hindu missionaries over there ASAP! 
America could become quite the powerhouse down the road, once they get in contact with the rest of the world and begin trading for some resources. I want to make sure that they're on the good guy team as proper Hindu devotees.
Sure enough as I predicted a couple of turns ago, my efforts to convert Mansa Musa back to Hinduism have proved successful. He's reached an almost sycophantic level of friendship with me now:
All the way up to +15 with Mansa Musa, wow! 
I'm only at +8 with Hatty. This is about as high a level as I've ever reached with an AI civ. There's no way Mansa Musa will EVER declare war on me right now, not unless something happens to worsen our relations. Since we're the two strongest civs on the planet, things are looking pretty good for us right now.
As for what I circled in the picture, the symbol circled in red indicated that I have Open Borders with that civ. I have Open Borders with everyone except Caesar at the moment, who refuses to trade with me due to religious differences. The yellow circle is around the symbol indicating that trade is possible with this civ; I can trade with everyone except FDR, since I'm separated from him by ocean tiles. Once I discover Astronomy, I'll be able to trade with him too. The other symbols on the score display indicate - as you've probably figured out by now - what state religion each civ is running.
My missionaries continue to pursue my goal of spreading Hinduism far and wide; one of them has traveled all the way to America and converts Washington:
I get a Great Merchant for being the first civ to discover Economics, but while I'm moving him across the continent to Timbuktu for another trade mission, I'll have to drop my science to 90% temporarily. 
Once I get some banks up, I'll be in better financial shape (I'm really not in any trouble at all, but was hoping I could keep running at 100% research). Discovering that tech has also opened up a new civic, Free Market, which adds an extra trade route to each city. I revolt to that, so let me show you what Mecca now looks like:
Our primitive city from the early game has grown into quite a metropolis now! As far as identifying things go, take a look at the trade routes first of all. I now have three of them, contributing a sizable 15 commerce each turn. I can get one more trade route, for four total, when I discover the Corporation tech, which I'll do pretty soon. Trade routes = money and research, so they are quite important. In the column below that, look at my shrine income. Up to 19 gold every turn now, and still climbing! I should be able to get over 30 gold once I finish converting all the American cities (though that will take a while).
As far as Great People go, I'm clearly about to generate one soon. But just what type that will be is anyone's guess. This is the one result of building a lot of wonders in one city: there's no guarantee what kind of Great Person you'll get. Still, usually better to do this and get more Great People than worry overmuch about the type. Oh - and there's the Great Merchant I merged into the city earlier. You can see what he's contributing to Mecca each turn too.
Since Timbuktu is a larger size now than before, I get more money from this trade mission. With the additional 1700g, it's now easy to run 100% science again. On a side note, I've certainly gotten a lot of Great Merchants this game... that's really quite unusual. I'm going to try and generate a Great Scientist next, because I could use an Academy in Mecca.
By 1330AD, with the completion of a Bank and Grocer in Mecca, I'm back to making money at 100% science. My Hindu shrine is paying for the entire costs of my civ, all by itself!
It's all about the shrine income, baby! 
Also note that I've finally gotten around to founding another coastal city to make use of some tiles that were otherwise going to waste (I should have founded Kufa much earlier, but wasn't really thinking about it). The next goal will be to get some colonies overseas on those islands I've discovered; with such a huge treasury and still running in the black, I can clearly afford it, and if I can get a Forbidden Palace over there, I wouldn't even have to pay that much in maintenance. That's the plan, anyway...
Meanwhile, my long development of the city of London has come to fruition. It's now designed as my super Great Person city. Take a look:
Thanks to the ridiculous accumulation of seafood resources outside London (3 fish, 3 crabs), I can run this city as a Great Person factory. Using Caste System, I'm now supporting eight scientists! I could get that to 11 if I wanted to, but I want to preserve some production in the city by having it work the mined hills tile and marble quarry. (My personal record for number of specialists sustainable in one city was 15 merchants during a testing game.) Since the city also gets +250% to Great Person points (Philosophical civ + Pacifism civic + Parthenon wonder), I'm up to a crazy 84 GPPs each turn. That will get me some Great Scientists for some Academies awful soon! Always fun to specialize cities like this; see what the land can do for you and use it to your advantage.
Now that I have a fair amount of the globe scouted out, let's look at the globe view. The button for it is in the bottom right corner of the main screen (it looks like a globe, shouldn't be too hard to find). This is what it looks like:
Yep, so it's an actual globe that you can look at and view. Now of course this is just a graphical effect (the maps are really still square and not spherical), but it does look pretty cool. You can also look at a couple of different filters on the globe; I'm using the cultural one now, and you can also view the globe by religion, look at resources, military units, etc. A fun piece of eye candy.
A couple turns later, I finally generate my first Great Scientist:
The special ability of the Great Scientist is to create an Academy, a building that increases science by 50% in the target city. It's very useful to put in your top science city, or even cities if you get a number of Great Scientists. They are also quite useful to use for discovering techs late in the game (or adding a lot of beakers towards techs). Mecca's research went up by about 40 beakers from this Academy, and that benefit will continue to add more beakers over time.
Shortly after getting that first Great Scientist, I pop another one as a result of running all those scientists in London. Let me show you what I mean by having a Great Person knock out most of the beakers towards a tech without discovering it entirely:
In this case, the Scientist only knocked two turns off of my research, so the effect was not that dramatic. However, the later you get in the game, the less the long-term benfit of things like merging a Great Person into a city or building an Academy matters, and the more useful the immediate rewards of discovering a tech become. A long-term effect does no good when the game is about to end! You can also save Great People to trigger a golden age, which is what I'll try to do next with my Great People.
With the discovery of Scientific Method, I enter the Industrial Age and all my cities change their look again. Also my workers now have the modern graphic to represent them (they look like little factory workers now). I'm actually beginning to get close to the end of the game here, it's about 2/3 of the way done! I'm still actually missing Gunpowder however, so I make a short pit stop to pick that up. And yes, you can skip techs like this and be in the Industrial era without Gunpowder.
Things have been too quiet lately. Now I don't particularly want to fight a war myself now... But why don't I get the AIs to fight each other and mess themselves up? Let's see what it would take to get Mansa Musa, who's pratically worshipping me, to fight with Gandhi:
It costs me an arm and a leg, but I'm way up in tech by now and can afford to give these techs to Mansa Musa. I don't know exactly what will happen next, but fireworks of some kind are bound to break out. I better start upgrading my defenses just in case some fighting breaks out with Gandhi!
In fact, no sooner does one turn pass before Mansa Musa comes asking for my help in the war against Gandhi:
Uh-oh! That's not exactly what I had in mind when I paid him to attack India! 
But if I refuse to help out, my relations with Mansa Musa will drop precipitously. What to do, what to do... Choices like this are what make Civ4 a fun game to play. Ultimately I decide we need to help out our friends. Gandhi has never really been my ally, while Mansa Musa has reached a ridiculously high level of relationship points with me. Let's join our Hindu allies and punish the Buddhist heathens! I accept Mansa Musa's offer to declare war.
Things just got a lot more interesting!
Next time: War! The Hindu team versus the religious unbelievers.
