How to revolt and win quickly in Sid Meier's Colonization?

Here's a speedrun I recently recorded (as discoverer) for a revolution in less than 7 minutes (26, or 27 game turns xD).
The only real remaining optimization I see here is to have the king surrender 3 turns earlier, which I got a few times. I suspect it might happens if your colony wasn't captured (which is pretty hard, or rather, luck-related, when you use a minimalist army).
Without a particular luck, you can't afford to sacrifice units to defend. Of course, retrying until a lucky run (ft. big early treasure) happens, but I prefer reliable and reproducible ways.

Since the thread Dylan pointed out is dead *off topic, I'll give in my two cents about playing on higher (i.e. Viceroy) difficulty
EDIT : now also speedrunned, in less than 15 minutes as Viceroy, as I'm editing the post. That game is easy after all ^^

-When I was young, I did craft many goods, start with Minuit/Hudson, sell furs, coats, rhum/cigars/clothes, kiss the ring, fear my fellow europeans, and so on.
-recently, I decided to try the game again, ahhh, nostalgia... I enjoyed it. a lot.
-But things changed. Here's a rough idea of how I go NOW :

• I don't usually alter land masses or climate, but for best results, continent-large land mass seems to be the obvious best choice to me. The main reason is you'll have much more lost city rumours (and indian settlements) to explore, which yields outrageous ammount of golds.
• If I want the best results, I take dutch. This isn't necessary, but I assume it should be if you aim for the fastest win. (except if you use the infinite money trick (see end of post), which requires playing anyone else, and is indeed faster... but feels a bit extreme to me. Well, thats another story.)
• When simply aiming to win, I noticed dropping my starting troops to rush an european, (in fact, usually two, and sometimes the 3) works pretty well. Players start at Y-positions 14/28/42/56. On generated maps, you, are either at 28 or 42 (middle), so depending on what you aim for, you know where to find one or two.
  Removing one of the guys already gives you roughly 50% of the territory for you ONLY, and a lot of free (and often skilled) colonists. You also usually get a free soldier (he funds a settlement), and his muskets, which is pretty useful, since you can let him stay on place to get the forthcoming replacement colonists, while your soldier can go take a 2nd extra set of muskets ^^.
  
  Though, speedrun-wise, you'd better focus on exploration.
  The europeans may be ignored, or exploited for some free gold : just threaten them every turn with a scout harrassing their mayor, and they'll often give 100-200 every turn. Yup, even as Viceroy !
  the point of disabling the europeans is also not to get flooded with retarded dragoons everywhere on your territory later, which doesn't matter here.
• if you get cool indians, trading tools&trade goods might still be of value. Some pay more than 1500 for their first tools. It's just very random. Well, on the other hand, your ship should be very busy... depends on which tribe(s) you find. Trade also lessens tensions, so you may consider giving one unit of #whatever sometimes (utterly lame, but very efficient :)). Personally, I consider trading isn't worth the hassle (except for the 100 starting tools, which easiens the recruitement of my first scouts)
• I don't bother crafting anything. My colonies already produce some free (and more often thrown for a fur-party than sold) fur anyway. My guys are more or less all producing bells to get the few useful founding fathers and the 50% bonuses useful to... get more bells xD
• Since I don't bother crafting anything, I need another way to get some cash. Buy ponies @europe on your first trip. If possible, get 2 scouts immediately (selling starting tools often pays for it). Else, get the second as fast as you can. Those guys have a ridiculousely high yield, for 100~150 gold only. Go scout every indian village you see. (use criminals if you have some, since they'll get promoted directly to expert scouts very soon). Some indian willages give more than 1K gold when you visit them. Exception : you may prefer skipping the Arawaks, since they tend to tie you up as archery targets (bug ???)
  When speedrunning, I now avoid buying more than 4 scouts (I used to buy 10-12, and carry 4 of them to the far edges of the world using privateers, but it takes time, raises mounts cost, and is in fact unnecessary)
• I don't enter lost cities rumours until I get De Soto. They might give something worthy, but will usually just suck. Once you get him, you'll get plenty of cities of Cibola (read 4K to 7K treasure) and fountains of youth (8 free and manually chosen colonists !!). Another thing which makes your experts scouts outrageously efficient.
• The first thing I used to spend money on after 2 scouts was some privateers. For a speedrun, it appears they are too expensive, but they remain incredibly powerful for a "vanilla" playstyle. I usually tried to stop after 4, since the game "seems to drastically increase their odds of sinking when you have too much", but they are clearly an abusable ship. Even just for transport or scouting, they are just too awesome. Getting free muskets or valuable goods is the icing on the cake :p
• Once the (new) world is mine, I peacefully wait for my scouts to get all the gold they can, then buy an army. Here's my current pick for a win : a mountain, ~20 dragoons (avoid servants and criminals as much as you can), 3 (or 4) galleons filled with ponies, and 6 artilleries. Farming indians can be an efficient way to get lots of gold, but except if you drop on aztecs immediately, exploration might be enough. Yet, it remains a good way to get veteran soldiers at low cost.
• Fortifications are a complete waste of time (and resources). You have to attack the REF troops with the (insane) ambush bonus. Never let yourself get attacked. (also, for that reason, I don't cut any forest aside water anymore. Ambushes are too precious.
  For a "fastest possible run", keep only one colony, near a mountain where the REF will drop all his troops. (the drops seem to work as follows : one Man-o-war chooses a (random ?) water square around your colony to teleport, then selects one (or more) of the free squares to drop army on (or drops over your -- now-captured -- troops). If all your water squares are adjacent to your mountain, just put a colonist on every other possible place, and the REF will happily jump into your trap.
  The only case where I let myself get attacked is when the RNG decides I'll fail all my attacks. That's the only reason why I added some (cheap and solid) artillery to my initial build

• I rarely accept more than 2% or 3% TOTAL as taxes (and prefer sticking to 0%.)
  Taxes are deduced when you get treasures, which makes exploration less abusable. Bad !
  Anyway, crafting good consumes precious time, and unless you protect them in wagons or ship every few turns, they'll get thrown if you don't accept a (usually too high) tax raise. This might be more questionnable when trying to win fast, but after completing several games in less than 1h30 on viceroy, I don't accept them more than usually.
  The only really annoying party is "horses". Since it's usually good to breed some everywhere... it tends to provoke it quite fast. For a normal game, I would recommend using Fugger as a "finisher" (i.e. to spend 30-40K buying and filling galleons just before declaring your independance).
  For a speedrun, just never keep unequipped muskets or horses in a colony before you declare independance

• The FF I hope to get, in that order :
  Luxury : De Soto, Cortes (mainly for Cibolas), Jefferson (skip him for a speedrun, he's not worth it before 5/6 fathers)
  Good : Brewster, Pocahontas
  Cool but unnecessary : Drake, Magellan, Minuit
  Too late : Bolivar, Washington, Stuyvesant, Smith, Fugger, Las Casas
  Useless : most other
  Negative : La Salle (stockade kills your flexibility.) , Paul Jones (a frigate is rarely useful, and I'm afraid increasing your navy reduces its efficency), Franklin (I dont want to prevent my king from giving me ¤500 and one or two goons for a war)

• Much more to say but... hey, I didn't intend to write a FAQ or guide ^^ Guess the question inspired me a bit too much.

[Useful exploits]

-- Flow of fountains --

The RNG in that game has some predictable patterns.
Avoid exploring rumours when one just gave something bad. And be sure to explore some more when you just found a fountain.
Keeping some scouts asleep near rumours will easily give you streaks of 3 or 4 fountains, which is enough to recruit an army when speedrunning. Also works with the (dangerous) burial mounds, not very interesting middle-range (~200-500 gold), or crappy "nothing" and "~50 gold" rewards, among others. very rarely with Cibolas :'(
Btw, when you get a bad reward (or unneeded fountains), consider doing many other actions triggering the RNG before you visit another.

-- Infinite money exploit --

Needs only 4 settlers and a ship at your european docks, cheap tools (they start at 1/2 and shouldn't have risen), and enough money to buy 400 tools.
The trick is that horses/tools/musket prices don't fluctuate when you equipp or unequipp colonists waiting at your docks.
Hence, you may equipp 4 colonists with tools bought at 4*200, then buy 1 tool twice with your ship (price rises twice), and sell the tools back at 4*300. Profit : 4*100. Every 200 tools bought, you may rise the price once more (up to a max of 8/9), which will quickly turn the benefits to big values (10*400 with only 10 colonists). Just sell back the single units of tools bought with your ship once your guys are desequipped to get tools price back to 1/2. (if you seem to get stuck at 2/3, consider training and unequipping a hardy pionneer).

Note that you should'nt have to buy much colonists when using this trick. Fountains should have already given you at least 8 (prefer 16 or 24).

Doesn't work as dutch, since prices don't collapse as fast as they rise, making you unable to get your tools prices down to 1/2 once sold. Doesn't seem to work as Discoverer, since the prices seem to rise faster than they collapse (same idea as playing Dutch). I didn't check the intermediates difficulties)
And doesn't work with ponies either, since their price drops faster than it rises.
Interestingly, this is exploitable in another way : just sell back your ponies everytime the price rises after you bought some, and it will stick at 1/2, at no cost (unless you accepted taxes, btw)

TL; DR :
Step 1 : Get some scouts & De Soto, explore a whole new world, buy an army.
Step 2 : ???
Step 3 : Profit !

If you wanted the Fastest run, you could try looking around the civ fanatics speedrun thread, and seeing some of their scenarios. You may also want to check out some of the strategy guides for some ideas.

Generally, a fast way to win is to find a nice settlement with lots of fish and a lumbermill, and get a scout/guns with your first shipment. You'll then be on a mad dash to gather as many guns/horses as possible (mostly from the indians you scout out). After you have lots of guns, grab some statesmen, get some citizens from Europe and turn them into dragoons, then revolt. You should be able to take whatever Europe throws at you.