The time of research depands on the number of techbeakers needed and the number of beakers you get every turn. To see how much beakers you need you have to change the science slider to zero. The number of turns discovering the next advance is the number of beakers you need (don't forget to set the sliders back as it was before you checked the number of beakers).
To do faster research you can do the following:
- move you're workers on tiles which have the most arrows (don't forget that you need enough food for growth and shields for support)
- set the slider for science to max (e.g. monarchy is 70%)
- build sciencebuildings like library, university, superhighway
- you can build a super science city (SSC). With the sciencebuildings and the wonders Colossus, Copernicus, Shakespeare, Isaac Newton and SETI and getting the city growing to maximum size you get an huge number of beakers every turn (do a search on SSC on this forum to get more details)
- Trade deliveries of caravans and freight. Each delivery gives gold and the same amount of techbeakers (until the max number of needed beakers is reached...after that moment you only get gold). Delivering caravans or freight from the SSC gives the most gold and tech beakers (delivering on another continent is best and to the AI (before you're cities have all the buildings). Trade deliveries gives also traderoutes (max 3 for every city). This will give extra arrows=extra beakers.
Hope this will help you a bit.