1. Build a city near many water squares.
2. Build a Library.
3. Build a University.
4. Build a Courthouse.
5. Settle a Great Thinker.
6. Grow city as large as possible, able to utilize every square in its zone of influence.
7. Switch to Democracy.
8. Customize your city's worker allocation to maximize Science.
9. End turn - Your science value will not be recognized until the next turn!
Civs that work best:
Aztec (Medieval bonus: Temples provide +3 science)
Japan (Ancient bonus: Sea squares provide +1 food. This allows you to build a city surrounded by as much water as possible but still grow.)