The most basic classification of flowers is into monocots and dicots.
In monocots, a single leave emerges from the cotyledon and the leaves have parallel venation. They have a fibrous root system. Petals and stamens are in a combination of three. For example, lily, tulip, orchid, etc.
In dicots, two leaves emerge from the cotyledon and the leaves have reticulate venation. They have a tap root system. Petals and stamens are in combinations of four or five. For example, rose, daisy, marigold, etc.
Flowers can also be classified as:
Annuals: These are plants that complete their lifecycle i.e., germinate, flower, produce seed, and die in one year. For example, asters, carnations, snapdragon, etc.
Biennials: They complete their lifecycle in two years. They bear roots, stems, and leaves in the first year and flowers and seeds in the second year. For example, hollyhocks, foxgloves, etc.
Perennials: They take about two years to produce the first flowers and then keep flowering every season for many years. For example, iris, lilies, etc.
Ephemerals: These plants grow when the conditions are appropriate such as adequate sunlight and rainfall; hence, are short-lived. For example, daylily.