How can companies determine that something is hypoallergenic?

Animal studies. This is usually performed on animals inbred to be more susceptible to allergies. The standard lab animals for such studies are mice, guinea pigs and rabbits.
Hypoallergenic? Many products are marketed with the term hypoallergenic on them. This term has no legal or technical meaning or definition. It is generally a claim which does not require substantiation. Terms such as allergen free or non-sensitizing may be more helpful and refer to actual analysis by the company such as human or animal studies. As far as i know none of these terms have a strict legal definition.