People classified plants by seeing if they have flowers or no flowers, internal or external structures of plants. They also classified if they were shrubs, trees, undershrubs, and herbs.
300BC-1400's Medieval Age
This period is also called the Dark Ages that lasted until the Renaissance. Albertus Magnus was the one that kept the science of plant classification alive. He classified plants by nonvascular and vascular.
1400's - The Renaissance
During the Renaissance explorers started to explore and travel to places. The explorers would bring back plants that they found and scientists started to rethink about the classifications they made before.
They started to write books about the way Andrea Cesalpino classified plants. Cesalpino wanted to classify the plats by how they relate to one another instead of by the colors of the flowers and the type it is.
Caspard Bauhin favored the progression of a plant's form from the simplest form (grass) to the most complex (trees). In 1686 John Ray based the way he classified plants by observable physical similarities and differences. Augustus Quirinus Rivinus classifies plants by the flowers and fruits that grow on it.
Carl Linnaeus examined the reproductive parts of a plant and classified them by that. That is the same way we do it today.
1800's Darwinian Era
Charles Darwin published a book called "On the Origin of Species." Darwin also claimed the species changed over time. He believed that there can be a variation within species.