You just need 20 great people. It pretty much goes hand in hand with the economic and technology victories. Certain economic goals give great persons, 1st person to discover certain technologies get great persons. Certain wonders built give great persons and certain ancient wonders discovered give great persons. You can also use spies to steal them from other cultures. Building wonders also counts towards the 20 person count. Each wonder counts the same as a great person.
Certain factors attract certain great people. There should be a guide online that will help you if you need more advice.
