Most people are sensitised by contact with their own pet. However, occasional contact with other animals can also trigger an allergy such as school pets.
The initial action when dealing with an allergen is to evict it. However, this is not always possible as the offending allergen may come from a much loved family pet.
To ease the allergic reaction the pet should at very least not be allowed in the bedroom and regular washing of the animal can reduce the amount of allergen released into the air.