1. Build improvements that increase culture (temples, libraries, colosseums, cathedrals, universities, research labs)
2. Build wonders (The Oracle, The Great Library, etc.) In case you have not played any civs before, they are listed in the manual and are located under wealth in the production bar.
3. Build them fast (once the culture structure has been built for 1,000 years, its culture doubles. This can only occur once to a structure and you have to build it before the year 1050 to get the bounus.
4. Destroy other leading civilizations with high culture (if you are militaristic)
*You can download a reference book containing lots of information about the game's improvements and units in the download section of this site.