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Other than that, the only things I can think of are building more cities, and putting more emphasis on commerce production. For the latter, make sure to build roads where your people are working, and use the Republic or Democracy governments if you can.
Republic and Democracy are ideal for science because they increase the commerce production of tiles that already produce commerce.
As for lengthening the game's turns, you can adjust the turn limit to a maximum of 1000 by going to 'Game Limit' on the very last screen where you pick your Civilization before starting the game.
There are plenty of structures that help with advancing Science such as the Library. Certain Civilizations also have a trait of 'Scientific' that helps speed their progress in advancing science.
This is just the starting off point though. As you play more you will understand how the game works. Read information on everything and only do things that make sense.
Not sure if you understand exactly what Scientific does. The primary benefit to it is that those civs get Libraries, Universities, and Research Labs half-cost - so the trait doesn't directly speed science advancement, but it helps you build the things that do faster.
It also gives you a free tech for each of the three new ages, which can be pretty nice, but that's a comparitively minor benefit.
From the perspective of the OP, I was simply trying to think on the basis of going 'all-in' for advancing Science. Of course, the 'Scientific' trait does not ensure a quicker advance because of the many variables that are incorporated inside the game like going to war.
1) Increase total Science spending. The amount of money you are able to spend is limited by what money you can generate. So the the more towns you have, and the the more working population in those towns increase your spending power. The quicker you can improve a tile to be worked the better (improve means build a road and mine / irrigate and later in the game build rail roads). This covers two of the key aspects of the game, quickly expanding your empire through settlers / conquest and devoloping your land / increasing population by workers. You should have as a minimum at least 1 worker per town.
2) Increase total science spending later in the game. When your empire expands the furthest towns suffer total corruption (all but one shield is lost). These towns should maximise population by producing as much food as possible by irrigation and then the town is able to support a number of Scientists adding to your total science spend.
3) Increase science spending through improvements. In core towns (suffering little corruption) build libraries, universities and research labs when available. Do not build these improvements in fully corrupt towns.
4) Government type. Get out of despotism as soon as possible as this is a poor type of government, losing shields, food and money. Your earliest choices are Republic or Monarchy, and as a general rule good players will choose Republic and stick with this to the end of the game.
5) Spend more on Science than on Entertainment. The more you spend on entertainment the less you can spend on science. So connecting luxuries, and multiplying their effect by marketplaces should keep your people happy, and let you spend more money on science.
6) Trade. Dont reseach all the techs yourself. Send units out to meet other Civs and trade for techs. Try and get a monopoly on a tech and trade with many civs on the same turn for Techs you don't have.
7) Extortion. Demand techs from weaker civs and if they dont give them to you then war is a possible choice. After a sucessful war demand their techs as part of a peace treaty.
8) Play a harder difficulty level. On the lowest levels the AI has a very slow research rate, but on the the highest levels their research rate is impossible to keep up with. The higher the level you play, the more techs you can get through trade.
There are other things as well, popping goody huts for free techs (Expansionist civs with scouts are best for this - huts wont produce warriors). Building the Great Library for free techs up to Education - but ultimately this is not a tactic to depend on.
I hope that helps.
EXPLORE (my favourite thing to do in general!), make deals but don't annoy people if they and/or their allies could easily kick your butt, try and stay out of wars, trade luxuries and stuff for money/happiness so you have more resources to devote to science, and make buildings such as libraries, universities, etc. Also in Civ 3, often having a great culture can flip the enemy cities up against your borders to your side for absolutely free--take advantage of that. :)
My only disappointment with the science tree is that it doesn't go into the FUTURE! I've always wanted a Civ game where you start off with one pathetic little settler thousands of years ago, and then later on, in the same game, with YOUR ORIGINAL SAME PEOPLE, you get to space elevators, wormholes, etc. (IF you live that long.) How cool would that be?
(Insert people mentioning Beyond Earth, Alpha Centauri and possibly even Call to Power here. I guess that last one is the closest we'll get to what I'm talking about, but it's not considered an "official" member of the Civ series.)