Army Prestige: Have a huge army, obviously.

Fleet Prestige: Have a huge fleet, obviously.

Economy Prestige: High economy prestige seems to be related to the economic buildings you build; i.e., the ressource buildings. You need to build these up to the top levels (which means you need to tech up).

Tech Prestige: You get some prestige from researching the philosophy techs, but the main prestige boost here seems to be related to the high level city buildings (note that many of these buildings also indicate a prestige bonus) and perhaps the level of your schools/universities.