I play vanilla, and have been doing this recently. I play Monarch level, with Peter, and it's surprisingly easy (will have to move up a level or two). Do what oyzar said, that's basically what I do.
Settle next to fresh water. Food and hills are most important in your BFC. Build worker first, while researching the relevant food tech. Then research masonry. Build a warrior second, then the pyramids. Chop forests outside BFC. Grab Bronze Workking and Animal Husbandry if you need them, hook up copper/horses if available. (If they're not, you'll need Archery.) Switch to representation when pyramids finish. Then tech to mathematics, build library, aqueduct, Hanging Gardens. When great people start coming in, settle all of them except one scientist (academy). Then tech to Literature, build Great Library. Tech Drama, build theater and Globe Theater. Don't forget National Epic. (In vanilla, you can build as many national wonders as you want.) Then tech to Civil Service, switch to Bureaucracy and Caste System. Run as many scientists as possible. Your goal is to pop mostly great engineers and great scientists, though an occasional great artist is inevitable and okay (the gold is useful). Then tech Paper, Education, Philosphy. Build university/Oxford. Switch to Pacifism if you can safely adopt a religion. Then tech to within 1 turn of Liberalism. I'm usually way ahead in (relevant) techs at that point. Then trade/tech up to Economics for the great merchant, finishing Liberalism whenever necessary. Take Nationalism or Astronomy from Liberalism. (Better players than me can probably get more for this.) Finish Economics, then tech to Physics for great scientist. Then take Electricity and Radio, build Broadway and R+R for trading resources and to get your last border pop a bit sooner. Then beeline Fiber Optics. Trade for the techs you're skipping so that you can get Assembly Line just before you get Fiber Optics. Build Ironworks when available. (I don't trade much at all before Literature, and only very specifically after that.) After you build your factory/coal plant, build the Internet. At this point you'll get all those techs you skipped for free, starting with Archery, Monotheism, etc.; it's pretty amusing. Build the Apollo Program (if you haven't already), keep teching up the tree, and build your spaceship parts. If your city's at the right latitude, consider saving a great engineer or two to build the space elevator. (But you shouldn't need it.)
In Vanilla/Monarch/Standard size map, this gives me a spaceship win in 1950 - 2000 range. Just pay attention to diplomacy; give into demands from dangerous civs. I never have to build too much military; sometimes I never build units more advanced than muskets. (Though I may upgrade my muskets late in the game to mech. infantry with all my extra cash.)
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