Once you’ve found the statute applicable to your research, use the Code of Federal Regulations for the final codified regulations promulgated by agencies for your statute.
You can also find an agency's final rules, proposed rules, and notices of rulemaking in the Federal Register. By browsing the agencies page of the Federal Register you can find significant and recent regulations published by a single agency. Here’s an example of the USDA’s Animal Plant and Health Service regulations page.
Agencies provide useful resources for interpreting their regulations and ruling authority - on their respective government websites.
Almost all U.S. federal agencies have some form of regulatory authority over animals. The main administrations include the Department of Agriculture, Fish and Wildlife Services, National Oceanic and Atmospheric Administration, National Park Service, the Food and Drug Administration, and the Center for Disease Control.