The large family discount is applied directly on iberia.com. Just select your particular category and the discount code during the purchasing process. This subsidy is granted by the Spanish government and does not apply if you choose to pay for tickets with Avios.
If you are travelling on the Air Shuttle or on a flight with Iberia code operated by Vueling you will have to book by telephone(+34) 900 111 500.
The large family discount only applies if all the passengers in the booking are eligible for it, if the booking only includes domestic routes and if the holder's status is valid until the end date of the trip.
Remember, you will need to show your Large Family Card when you check in or board, so remember to bring it with you along with your other travel documents. Iberia will be obliged to deny boarding to passengers with discounted tickets who cannot show their card.