The EBT food stamp program is a component of the federal Supplemental Nutrition Assistance Program, which is overseen by the United States Department of Agriculture. Each individual state maintains its own food stamp program, but a general overview and links to application pages can be found at the USDA website.
The USDA does not process applications directly, but it does maintain a directory of links to the online application for each state that has one. As of April 2015, 41 of the 50 states allow their residents to apply online. States generally maintain their own individual websites that describe the specific terms of their program.