It's been a while since I played the original Civ, but I still recall that the following worked most of the time for me:
In the early stages of the game, put science up to the highest value you can sustain, get Monarchy (at least) and switch to that type of Gov't as it improves productivity. Try and get the advances needed to build the Great Library, and make that your first Wonder of the World. It lets you ride on the back of other civilisations' discoveries, as you automatically get any advances that two others have.
Then aim for Railroad, and once you get it, cover your land with tracks (again, it improves productivity, but it also lets you have unlimited movement along the rail line). After this, switch the emphasis to making money, rather than advances.
With the money, use diplomats to buy opposing cities (no need to fight them, use the miracle of economic warfare). Buying a city also lets you choose one advance out of your opponents list, so you can still advance without spending big on science.
I've actually won quite a few games by buying all of everyone elses cities (apart from the capitals, which you have to crunch).
Civ 2 is harder though. The diplomacy thing doesn't work as well.
Regards
David