Civilization V has grown over a few big expansions to become one of the very best games on the PC. I'd go so far as to say it's *gasp* the best Civilization game of them all. To help out newcomers, then, or just those who are upgrading with the expansions, I thought I'd put this guide together, letting you know some of the best tips to keep on top of jerks like Gandhi.
Note: this guide, originally published in 2013, has been updated to add more tips and cover advances in tactics/mods.
This isn't a complete and thorough guide to the entire game; we don't have the space or time for that. Think of these as some golden rules, to help guide you in the right direction. Note also they'll be covering tips for the entire game, not just the latest expansion.
START SMALL & EASY
While it can be tempting to start your first games on a large map, you're better off starting on "small", or even "tiny". The advantage of these sizes is that they not only cut down on the amount of "grinding" you need to do in terms of expanding and building, but they can also be more interesting games, especially if you cram 6-8 civs into them. Ditto for difficulty. Start at the bottom and work your way up; there are enough changes to the fundamental Civ formula with this game that even veterans need to dial it down a bit while learning the ropes.
The very first thing you're going to want to do is expand. The most precious thing on a Civilization map is real estate. The more cities you have the more gold and research you'll generate, the bigger your territory the more likely you'll be to own necessary strategic resources. So build settlers early (with the odd worker to build roads between your cities), and when adopting social policies, start with Tradition, which grants expansive bonuses. Don't stop expanding until you start losing money and/or creating unhappiness.
That last part there about happiness is actually worth its own section. You must always keep your civ happy. While in previous games having unhappy citizens wasn't that big a deal, in Civ V it can cripple you. At first, you'll suffer reduced production and income, but let things get out of hand and rebels will start popping up and trashing the place. While focusing on gold and production might seem tempting, especially to veterans of the series, I've found happiness is the first thing you need to worry about, because it's the hardest to stay on top of (trade routes make income a lot easier).
Religion might seem like a bit of fluff, but it can be a powerful diplomatic and cultural weapon, not to mention a good source of happiness for your own people. So as soon as you're done expanding, focus on building shrines and temples so that you can found a religion and start spreading it. If another religion overruns your Civ before you've had a chance to found your own, you'll be at a disadvantage for the rest of the game.
It's tough to pick one dominant research path, since it really varies depending on your play style, but related to my expansion point above, I've found the most beneficial to your long-term success is to be the first to get navigation. Whoever can venture across the seas first, potentially finding whole new and empty continents (or at least strategically advantageous islands) where you can double the size of your empire, has an enormous advantage over those civs stuck in the old country.
FINISH WHAT YOU STARTED
When it comes to social policies, it can be tempting to pick and choose from everything that's on offer. Don't. If you start down one tree, finish it. You might get the occasional boost from grabbing one policy from each choice, but you'll only get the really good bonuses by completing an entire social policy branch.
Don't ignore the new trade route system in Brave New World. If you've got four available trade routes, build four caravans or cargo ships. If you've twelve, build twelve. You'll not only make buckets of money from this, but it's also a good way to spread your religion (and get a slight science boost as well). If you can keep trade gold flowing for the majority of the game, by the industrial and modern eras you'll have thousands in gold.
GREASE THE PALMS
Previously, city-states were something to be tolerated, or even ignored. No longer. Now that they count as voters in the World Congress, the player who can ally themselves with the most city-states has a massive advantage, whether they're actively pursuing a diplomatic victory or just want to screw other players over. The easiest way to do this is ignore their quests and requests, and simply stockpile your trade gold. By the time the World Congress starts getting important later in the game, you can just buy their votes.
Don't just build roads between your cities. Build them densely around areas you muster your armies. Build them on coastal areas between continents you might need to launch an invasion from. Build them to nearby city-states. If you've got open borders treaties with your neighbours, build them to their cities. Why? Because eventually you're going to go to war with them, and conquer them, and having roads in the middle of a war (and everywhere your units are kept, letting them deploy faster) is a huge help.
Many of the game's mods are hit and miss, but one that I think is a necessity is the R.E.D. (Regiment & Ethnic Diversity) pack. It not only changes the scale of many units (more, smaller troops, etc) but like the name implies makes them more diverse depending on what civ you're playing as/against. So instead of there being one generic tank for all civs, for example, an American tank will be a Sherman, a Russian tank a T-34, etc.
While Civilization V offers you a vast variety of military units, for most of the game, you only need a handful. Whenever and wherever you're fighting, a mobile "turtle" mix of infantry (warriors, swordsmen, riflemen, etc) and siege weapons (catapaults, cannons, etc) provide the best mix. Ditto for naval combat. For much of the game you can get by with brute force, amassing an armada of frigates and battleships, which are not only dominant at sea but can also be a huge advantage for coastal warfare. You only need to really diversify (with air support, anti-air weapons and fancy airdrop infantry) once you hit the modern era.
DON'T SPY (MUCH)
There's always an urge to use your espionage units to spy on other Civs, but just because they're called spies doesn't mean they need to spy. Stealing techs can be slow, and dangerous, and only really useful if there's one Civ way ahead of you. In most other cases, it's better to split your spies between rigging the elections of nearby city-states, helping cement your hold over them, and employing them as diplomats, because buying votes for the World Congress is a lot more important than the odd free tech.
BE COOL, MAN
There's always the temptation to be a conqueror, constantly invading your neighbours. It's understandable, because it's fun. But if you're playing on a bigger map, with lots of Civs, it's just not worth it. You'll develop a reputation as a bit of a monster, and that's not a reputation you want to have when the modern eras roll around and you need to regularly count on other Civ's votes.
There's so much variety to be had in the game's Civilizations, so many perks designed to cater to an individual's play style, that saying a single one is better than others would be foolish. My favourite, though, is the English. The extra naval movement bonus you get is a big help when you're exploring (especially if it's stacked on top of other +1 movement perks like the Great Lighthouse), an extra spy can make a huge difference and the Ships of the Line unit is just a beast.
Seriously. He's the worst.
That about does it for the groundwork! The beauty of the game, especially since the addition of spies, religion and the World Congress in expansions, is that as complex as it is, there's fun to be had in experimenting and getting your head around the finer details.
Until then, though, hopefully these broader points will serve you well!