While I think it is a very honorable idea, the reasons why they put the animals down in the first place is because they are overcrowded. An overcrowded shelter is not a good environment for an animal. They do not get the attention they need. Food and shelter is just the beginning of an animal's basic needs.
As Slashnl mentioned, you also need to be aware of state/federal laws regarding these kinds of charities. You, most likely, will need some sort of license and a tax code. It seems like a lot of work to start, but if neglected can end up costing you thousands in fines.
This link may give you some of the answers to the more mundane aspects of starting this endeavor.
http://www.wikihow.com/Start-a-Charity
I encourage you to find a way to raise awareness about adopting animals from the shelters, and in general making wise decisions before buying a pet in the first place so they do not end up in the shelter. Population control is also important. Most shelters offer a reduced price on spaying and neutering, especially if the animal is a stray.