In order to make an inhalation, the easiest is to use a bowl of very hot water in which you put a few drops of an inhalation mix for cats. Place your cat in its pet carrier. Be careful to put the bowl in front on the box, and not inside it, as this will prevent your cat from trying to drink the water (and with it the essential oils) or burning itself! Cover the pet carrier with a towel.
If you have an inhalation nebulizer you can use the same technique and introduce the nebulizer’s mask between the pet carrier’s bars.
Make sure to wipe your cat with a humid cloth after the session. This will avoid it swallowing the essential oil on its coat when it grooms.
Find here the benefits of inhalations for cats suffering from the respiratory symptoms of cat flu.