What size map are you playing on? You will advance much slower on larger maps unless your civ is proportionally larger. Use a small map for a while, the games can still be a decent length and advancement is much faster.
Science is created by trade and of course scientific buildings. In cities that have good amounts of trade, build libraries, universites, and try and get one or two of the technology wonders. On chieftan you can actually get all the wonders very easily once you get a bit better.
Another thing is that you need roads and railroads - these will increase the trade you get on each square. The thing is, yo don't get the full extent of these bonuses unless you are a democracy or republic. Despotism gets a minus here, and I think monarchy and communism don't get modifications to what they get on squares. Communism is superior in almost every way to despotism, but if you aren't at war with someone, demoracy is much more efficent.
So - try and use the more advanced governments. Despotism has some good uses, but is inferior for extended play at a lower level, particularly if you are trying to win the space race (Where repub/democracy is preferred, althohugh I can outpace the others on Warlord in anything but despotism easily, without trading techs at all (With trading it is much easier to keep up even with 0% science)
Now - how many cities do you have? If you are on a large map and have less then 20 or so, then you have a tiny civ, and you will advance very slowly.
The key to advancing fast later in the game comes from setting yourself up properly earlier in the game. At the very beginning, expand, expand, expand. I tend to prefer expansionistic and religious for this reason - expansionistic gets you scouts, and while I generally only build 1, maybe 2 or 3 on a larger map, that extra exploration capability at the beginning is amazingly worth it. You can get settlers in goody huts, which can quickly turn the tide of the game in your favor, even on the third turn. With you main city, get a scout out then fortify a warrior, then make settlers like crazy, with an occasional military unit in between if you feel the need. On your second-fifth cities, do the same. The idea is to grab as much land as you can at the start of the game so you will have more good cities which will produce more stuff later on in the game.
So - expand FAST, try and build some workers while you are expanding, and get your civ nice and well roaded, and try and get the science or trade wonders (Colussus/Trading company also helps research - colussus through added trade, Trading co through allowing higher science), also don't forget to get libraries at a minimum in your decent cities.
Lat game I played on chieftan was on a tiny map, and I was making advances at 4 turns each, and pulling in a couple hundred gold a turn with a small military. The game I am playing now I am advancing once every 10-12 turns on Warlord in communism and have ~30 cities on a normal map, and a rather large military (About 100 mech inf, 40 or so tanks, and 50 or so cavalry on top of a small navy and a load of workers).
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