Sophie your Phalaenopsis can't be propagated like so many plants can.
As Australis mentioned, keikis or baby plants, sometimes form on the bloom spike and those could possibly be cultured.
You can't propagate by leaf cuttings or rooting a leaf like an African Violet. Since they grow from a single central stalk, you can't divide that either. It would kill the plant.
You have the option to pollinate a flower in order to get a seed pod. Growers do that commercially because it is expensive but they are raising thousands of seedlings. But it takes 3-5 years for professionals to do it and get plants.
For you to spend a few hundred dollars to get a few seedlings it would be much cheaper to buy new plants. It requires absolutely sterile conditions.
