I don't want to sound arrogant, but I have about a 95% win rate in multiplayer. With that said, here is my take:
First would be your civ selection. In a true duel map, as you have already found, the game is not going to be epic in length. Swords or Pikes are going to be the most dominant unit unless there is a pre-agreed peace period. Longswords will probably be the final unit that takes the other player out. You are also guaranteed to be going for a military victory. It would then make sense to select a civ with strong low-level UU's or strong early-game advantages.
Secondly, you'll want to completely and utterly disregard science if you wish to survive. You'll want to disregard buildings that you would normally have to build like monuments and libraries. Each of these buildings puts you behind 1 or 2 military units worth of production. You'll almost positively have to go with the honor path to get an early General and then either experience or additional flanking bonus (I'd take the bonus). You don't need to out-science your opponent because after iron working it really won't matter much since you'll go right for Steel or Civil (if you get no iron).
Next, you'll need to save every penny of your cash for unit upgrades so you should never buy any tiles around your cities unless it is an iron pile that you must have or are stealing from your opponent. You'll need to be in the constant mindset of 'kill or be killed'. Things like stealing a worker from your opponent early (even if you can't get it home, just delete it!) or stealing a city-state worker for your use can be game-changing. Things like posting warriors as 'attack-lookouts' or to fend off settlers is also key.
Keep in mind the playfield is critical. You have to completely dump your concept of 'proper city placement'. You naturally are going to want to settle next to luxuries and resources. You should completely throw that mindset out the window. Each of your cities is a step towards domination and you are militaristic, right? Your cities should be mini-forts designed to choke your opponent and defend against their advancing forces. Cities on hills with low-defense tiles around them are key. Desert, Marsh, Tundra- these are all very bad for defending units. If you pop a city in an area surrounded by hills and forests, unless you control those tiles, you are giving your opponent a huge defensive advantage while they are trying to sack your home! You should also chop out your settlers with any surrounding forests (even outside your borders). Stopping your city growth is painful enough, let alone the amount of turns to get a settler out.
Another easy tip to give you an advantage is that your third city will likely come very close to the time when you get iron working. Regardless of where the iron is, plop this city right on top of it. You immediately get the resource and the city really won't be much of a contributing factor going forward as your attack force should be ready to roll (warriors ready to upgrade and a pile of 300 gold in the bank). Even in quick, mining a pile can take up to 5 turns and that is a big difference- like you saw- you missed your upgrades by 3 turns!
Lastly, don't panic. Play smart and calculated. Don't get into a click-fest and accidentally move your units into squares they just left unless it is a sure kill. You'll end up putting them in the heart of battle with no chance to fight back and by click-festing you end up losing them altogether. Don't go buying a bunch of units with cash you should be saving for upgrading because you see more units coming than you have. Keep your defending units on defense tiles (hills, forests, etc) and attack their units of negative defense tiles (like march and desert). Little things like a warrior or spearman on a hill with a forest can really mess up an attacking swordsman. And of course, practice makes perfect.
Civs to play in a Duel: (Obviously people will have different takes, this is MY take).
China: You may be able to skip going honor path and get a General through battle (barbs/opponent) and use your social policies elsewhere to grow your cities or produce settlers faster. Your General is also stronger giving you more of an attack bonus. You'll also get a second one pretty quick once the battle really starts so you can replace a fallen General or pop a golden age to get extra gold and build units quicker. Unfortunately, going for the awesome Chu-ko-nu is almost a waste in a duel because you'll need Steel.
Russia: The extra production from resources and the double strategic bonus can really make Russia deadly, especially if there is only a 2-pile of iron and you get it! The increased production can help you pop out units faster than your opponent too. Unfortunately your UU is too far in to be of any help.
Japan: Likely the best of all duelists simply because there will be blood, and Japanese warriors don't back down. The bonus of hurt units acting like full units is ridiculously strong in a duel. If you can get to Samurais, you should win hands down.
France: Although you will never get to their UU, France's culture bonus can be a game changer too. You will get tiles twice as fast as your opponent and your new cities will not need monuments to expand. The math is simple, the money you will save from not having to buy any tiles, and the additional picks of good tiles from cultured area can be key to your success.
Germany: The barb encampment unit-turning and gold bonus can be very nice, but don't go chasing that and leaving your cities undefended. The bigger bonus comes from the Landsknecht, a strong early UU that can really cause some trouble.
Greece: Oh the pick of the cheapest of all Duelists! The duelist's UU dream come true. The endless Hoplite rush is truly overwhelming and when played right, Greece can be unstoppable in a duel even against the best defenders. If you attack early with your overpowered hoplites (you may even get one in a hut even!) and put your opponent on defense, just keep a steady stream going towards them. You can also just skip the whole iron concept because you'll want to go for your Companion Calvary which will prove purely devastating. I personally find Greece to be cheap, and if the player is good, the only real defense is Japan.
Aztecs: I'm not big on them, but the early UU Jaguar is pretty nice. Likewise, you know there is going to be battle and that culture bonus may open tiles and unlock civics that can change the war. They're not my first choice, but played correctly, they will do a good job.
Iroquois: Nice early UU and if you start with 'normal' start bias, you have a strong Capital advantage. You can chop until you are blue in the face and you start with stronger units than your opponents. But keep in mind, you will get outpaced quickly, so you shoudl plan an early skirmish to try and set your opponent back.
Persia: Immortals are wicked little monsters and they are available immediately. You're not very likely to get a golden age too quick, but if you do that is a nice benefit at 50% longer. Like the Iroquois though, you better exploit your advantage early if you hope to win. The classic Immortal Rush!
Songhai: These guys are teetering on the yes/no for me but more yes than no. If played right and given enough time, they can be awesome. But time is not something you get a lot of in a duel. The extra gold from encampments can give you an edge on upgrading and the fact that you will want to b-line right for their ridiculously overpowered Mandekalu means you are not iron dependent... but you are horse dependent. If you get horses though, spamming out horsemen (which is otherwise a bad idea) gives you highly mobile units that when upgraded will simply lay waste to your opponent.
Civs Not to play in a Duel:
India: People think the War Elephant is great. It's simply not. The happiness bonus is nice, but also not strong enough to make them a good candidate.
England: Likely one of the worst duel picks you can take. The Longbow is sweet, but by the time you get there you'll be dead.
America: Being able to see your impending death a few turns earlier isn't going to stop it.
Arabia: If you get to oil in a duel, you're doing something wrong. Likewise if you can get to your UU you're opponent sucks.
Egypt: If you are trying to build wonders in a duel, unless it is the Great Library, you're not going to win anyway, so feel free to pick them.
Ottomans: Likely the worst duel civ you can get.
Rome: Also just not a good duelist. In a normal game they are great, but you likely won't be building a lot of buildings in a duel and your UU's are too far out to take advantage of.
Siam: I don't foresee you making many City State friends in a duel. And even if you did, there won't be enough time for it to make a big enough difference.
HOPE THIS HELPS!
