It depends on what you mean by "address". Governments are the only ones who have power to make laws, so they should be the ones to create legislation that reduces emissions. Economists should be called in to assess the best way of going about that and to carry out cost/benefit analyses for the different strategies. Scientists (physicists, geologists, meteorologists, oceanographers, etc.) should be the ones who make accurate predictions about what the climate will do.
I suppose advocacy groups can help encourage people to be more sustainable and efficient--but honestly, a person who would listen to what the Sierra Club says is probably already pretty sustainable anyway.