This varies by animal and by state. Poultry under 20,000 birds per year is left to state regulation under the Poultry Products Inspection Act of 1957. So, for instance in Alabama, you can slaughter up to 20k birds per year at your state inspected facility. The rub is that in AL, you cannot gross more $200 from this activity, so the exemption is essentially useless. In any event, these birds cannot be sold interstate.
Cattle, swine, sheep, goats, ect. are covered under the Federal Meat inspection Act and its follow-ons. It requires any meat for sale to be slaughtered and processed at an inspected facility. It allows states to inspect facilities but the meat from those facilities can only be sold intrastate. If you wish to
sell interstate, the meat must be slaughtered and processed in a USDA inspected facility.
Here's a handy summary from California.
http://ucfoodsafety.ucdavis.edu/files/26481.pdf