There is no fix way by which you can fund a museum. Most of the times it is the territorial government that provides fund to establish a museum, but some times there has been some enthusiasts who come forward to fund a museum. They think and rightly so that a museum depicts the culture of an area and it's not only the culture of one particular era but how it evolved with the passage of time, all these things find an expression in a museum. And they think that as a responsible citizen, it is their responsibility to provide fund.
Sometimes they approach some big corporate houses and many a time it happens that corporate people themselves take initiative to fund a museum. It not only gives them a good corporate image, but they can make a brand recall also with this initiative as the name of their corporate house must be on a plaque at the museum.