There are two types of health certificates available: one which approves pets for travel within the continental United States, and another which approves them for international travel.
Acquiring a health certificate will require you to schedule an appointment with your veterinarian. Your pet will receive an overall exam during which the doctor will be able to certify that your pet is healthy and safe for travel. The doctor will also verify that the rabies vaccination is current, as this is mandatory.
Exact requirements for obtaining health certificates from your veterinarian vary greatly based on your destination's guidelines. It is crucial to research specific requirements well before your travel dates, as the time needed to obtain the certificate can range from a few hours to a few months (depending on your destination's requirements).
For international travel, you can research your destination's requirements here: https://www.aphis.usda.gov/pet-travel/us-to-another-country-export.
