The plant hormones are synthesised by the plant cells individually accordingly and when needed. Few hormones are specifically synthesised at a particular plant part, like auxin synthesised in growing shoot apices.
Ethylene is emitted by ripened fruits. Cytokinin is found in dividing cells. Unlike plants animal being more advanced, and organised they have proper hormone secreting glands and organs.
In both plant and animals these are transported through the transport system of their body. In plants, hormones are translocated via xylem and phloem to the site of activity.
Discovery of plant hormone gibberellins was made by chance. It happened by chance in rice fields. A few plants of rice were observed, which were unusually taller than the normal ones. Scientific investigation revealed, that these were infected with a fungus, known as Gibberella fufikuroi. This fungus releases a plant hormone gibberellic acid in excess concentrations which made the plant to grow unusually tall. This compound was later known as gibberellin is hormones present in all plants.
The term used for accidental finding is Serendipity which means fortunate happenstance. It was coined by Horace Walpole in 1754. He explained it as making discoveries, by accident and sagacity, of things, which were hot in quest of.