Here be a wall of text for the budding Leader of the Greatest Civilization on Earth.
Before Playing:
Consider the map type. The map type will have a large effect in your game. I suggest using Pangaea to get started. Or, simply, don't play with water (ocean) just yet. Water maps tend to go on for longer than land-heavy maps for a lot of reasons.
Check quick combat/movement. This will speed up your gameplay especially when there are a lot of units. You can set this option mid-game.
Civ Selection: I suggest go for Aztecs first if Vanilla. Ethiopia/Celts/Maya if you have Gods and Kings. The former for their ridiculously good UU/UB Combo and the latter since they will allow you to easily play with all the systems currently in place, Religion included.
Difficulty: Start on Prince. Anything below you would use if you want to dick around and build all wonders, for example.
So, you've clicked that play button and are now in your first game with your Settler and initial warrior. The options are endless! Should I settle here or there and what should I build and to research and why are those gentlemen in loincloths trying to bash my cranium in and OH MY!!!! Here's some guidelines and some tricks you can employ to help you.
Your first city: This is your capital, and like all great civilizations in history, most start near a bod of water. Mesopotamia had the Euphrates and Tigris, Egypt had the Nile, etc. In short: When at all possible,
settle adjacent to a river. Rivers provide +1 gold to every tile adjacent to it, providing critical in-game commerce. What's more, farms built on them will get +1 food once you get to Civil Service. Other considerations:
Food: You'll need an abundance of food to grow your cities. Food indirectly provides production, since it allows you to have citizens to work the hills. Food directly provides science with the help of your science buildings. This is the most important piece in the early game.
Some nearby hills: You'll need production to get anything done.
Luxury Resources: You'll need happiness to be able to expand, and to get Golden Ages. Usually, you will have multiple copies of one and another type somewhere nearby. Note that Luxuries provide happiness on only ONE copy, so if you have extras, sell/trade/bribe it away.
Jungles: Minimize jungles. You will need Bronze Working in order for your workers to be able to clear them, and even then, they require A LOT OF TIME to clear (just be wary that Aztecs have a jungle start bias).
Forests: On the other hand, are a big help. Chopping them down (available at Mining) will yield 20 production for a city. Helps greatly if you want to rush buildings/units/wonders in the early game.
Mountains: Those create a natural barrier and is a requirement for Observatories (which provide a science boost) and some wonders. This is the least important consideration, since you can achieve a very high tech rate even without it. Think of it as Icing.
The best starting location right now would be: Floodplains (basically desert tiles cut through by a river) or riverside Grassland with some Wheat Tiles, a few Hills, a one-tile mountain, with at least one hill with a Mining Luxury Resource. If you settle a city on a Luxury resource, you immediately get the Happiness benefit the moment the tech comes online. You can use the above to settle your other cities as well. You'll find that the above are not always present, so you have to weigh the pros and cons.
Technology: Your starting area will decide which technologies you pursue in the beginning. What I usually do is go Animal Husbandry first to check for horses (which you can sell to the AI), then Archery so I can build something to defend myself with when I run out of infrastructure to build and then go for the luxuries. Not necessarily in that order though.
Culture: Accumulating empire-wide culture will allow you to select Social Policies. Culture on a per-city basis determines how quickly your borders expand. The more culture your city generates, the quicker its borders will naturally expand, reducing the need to buy tiles. Take note that the more cities you settle, the larger amounts of empire-wide culture you need to get Social Policies.
Military: You can defend yourself in the early game with four archers. More as you go high up in difficulty.
City States: these provide bonuses your cities otherwise don't have native access to. Maritime provide food, and this accelerates the growth of your cities, especially your capital. Cultural provide additional empire-wide culture, allowing you to get Social Policies sooner. Military gifts you units from time to time. Religious provide Faith, which you need to found Religions and buy specific units and/or buildings. Mercantile provide extra happiness. Bonus levels depend whether you're friends (green bar) or allied (blue bar). You need influence to be either, which comes from Gold Gifts and Quests and returning captured workers. They also provide additional Science with the right Social Policy.
Handling Barbarians: This is why you need an archer or two in your home turf. You'll need to protect your workers from being kidnapped.
Diplomacy: You can't please everyone, so get on the good side of a neighbor or two, and don't be a lying dealbreaker. Sometimes, other leaders will come to you asking why you have military near their borders. If you say you're just passing through, don't declare war on them for at least 30 turns (there's an invisible counter for promises, just not so sure how long). Dealbreaking is declaring war on a leader while you have deals currently ongoing. Don't be triggerhappy either, or you risk being declared a warmonger and international relations will just break down.
Civ 5 is a different breed, since it's the first game in the series where a tall empire (1-4 size 25+ cities) can directly compete with a wide one (many cities with lower population per city.) I suggest you go Tall and try a Science Victory, since it will take you almost the whole way through the Tech Tree so you can see more of the game. Aim for a sub-350 victory (normal pace). I can give more tips if you want
