Create a will that specifies how your estate will handled. You can leave everything to the humane society, if you wish, simply make it part of the will. You can also name an executor for your estate - someone you trust to make sure that your instructions are carried out.

When you die, all your assets and debts become your estate. The assets will be used to settle any outstanding debts, and the remainder dispensed per your will. For real estate, it’s likely that the humane society has no use for the house, so you might ask that it be sold and the proceeds donated. This would be a task for the executor.