How much money does a humane society earn?

There are several layers to this answer. First, humane societies in the United States tend to be non-profit organizations, which means they can't earn money. They derive their operating expenses from fees for service and donations, but the income cannot exceed the expenses by all that much.

Second, the money flow depends greatly upon what level you are asking about. Local humane societies (the ones you can visit in your community and adopt a pet from) tend to work with several million dollars a year or less. National organizations such as HSUS work with hundreds of millions of dollars a year, but (at least in the case of HSUS) the money typically goes towards animal advocacy rather than directly helping stray or abandoned animals in your community.