This is the worst-documented thing in BNW. The theming bonuses for wonders and museums is NOT secret. You have to hover over the "+0" in the culture display screen to see the criterion for the theming bonus on that building. The value of the bonus is equal to the number of slots in the building (doubled in the French capital).
In the case of Museums, you can get half the bonus by almost meeting the criteria. That is, you get +2 if you have two art or two artifacts from the same era and either your civ or other civs. You get +1 if you have two art or two artifacts from the same era but one is your civ and one is another, or if you have them from different eras but both yours or both not yours.
AFAIK none of the wonders have a partial bonus option.
And in case you are asking for information that *is* in the manual or pedia, the short answer is that if you put things in the slots of a building that match its theming criteria, you get bonus tourism beyond that for the things themselves. You do not get bonus culture, only tourism.
