Place pig's feet in a large container with cold water to cover. Soak 3 hours; scrub with a stiff brush. Rinse thoroughly.
Combine pig's feet, onion, celery, 1 bay leaf, salt, and pepper in a large Dutch oven with cold water to cover. Bring to a boil. Reduce heat; cover and simmer 3 hours or until meat is tender and separates from bones. Remove feet from cooking liquid with a slotted spoon. Place in a plastic, glass, or stainless steel container with a tight-fitting lid; set aside.
Strain cooking liquid through a sieve; discard vegetables and bay leaf. Set cooking liquid aside to allow fat to rise to surface. Remove fat, and discard. Set cooking liquid aside.
Combine vinegar, cloves, and remaining bay leaf in a saucepan. Bring to a boil; reduce heat, and simmer 1 minute. Add reserved cooking liquid, and bring to a boil.
Pour vinegar mixture over pig's feet to completely cover. (Additional water may be added to cover pig's feet, if necessary. ) Set aside to cool to room temperature. Cover and refrigerate 24 hours.
Remove pig's feet from vinegar mixture; serve cold.