Rote memorization.

When I took plant ID, the courses were divided into spring & fall (this was in the Bay Area, so if something flowered during one part of the year, that was the semester it was taught).

We made flashcards for study aids. One side had a dried, pressed plant specimen mounted on it under clear contact paper. The other side had botanical name, common name(s), and other descriptive information about the plant -- family, genus, height, form, flower/fruit type, area of distribution, whether it provides food or habitat, etc., etc.

I also spent time volunteering at the local arboretum, and that was a great way to get familiar with the plants and how they look different throughout the year.