Some of this depends on whether you have Brave New World or not.
Vanilla/G&K:
Domination - be last Civilization in control of own capital (so take all other capitals or have AI take some of the other capitals and take his capital)
Cultural - Finish 5 Policy trees, build Utopia Project
Diplomatic - Build UN, get voted Supreme Leader (City States provide many votes)
Science - Build Apollo Project, research all technologies required for spaceship parts, build all spaceship parts and assemble the spaceship in a city.
Brave New World:
Domination - Take ALL Capitals
Cultural - Generate enough tourism to surpass the culture of all other civilizations (all culture generated since Turn 1 for each Civ) (Also note that Tourism only starts generating from when you first meet that Civ)
Diplomatic - Same as Vanilla/G&K (but votes are counted differently when you progress from World Congress to UN)
Science - Same as Vanilla/G&K (required technologies may have been changed)