Count the petals. If they are in multiples of three, you have a "monocot" a member of the lily class. If they are in multiples of five, or have many petals, go to Step 3.
If there are one or two stamens, you have a member of the orchid family. If more, go on to Step 2.
Count the stamens, using a magnifying glass or hand lens. If there are six stamens, you have a member of the lily family. This includes trilliums, fritillarias, asparagus, camas and erythroniums, as well as lilies.
If only three, it is a member of the iris family, which includes the genus Sisyrinchium (blue-eyed grass) as well as irises.
Decide whether or not your flower is in the daisy family, the Compositae. This is one of the largest plant families and is characterized by having a disk made up of tiny individual flowers without petals, surrounded by "ray flowers," each with a large petal, the whole group of them combining to give you a daisy shape.
This group includes chrysanthemums, feverfew, rudbeckia, echinacea, sunflowers and, of course, shasta daisies.
Decide whether or not your flower is in the legume family, the Leguminosae. These have distinctive pea-type flowers with a flat petal at the top, often called a "standard," two side petals called "wings" and two petals that have been fused together to form a "keel" at the bottom.
Count the petals again. If you have only four, chances are your flower is a member of the mustard family, the Cruciferae. These include dame's rocket, broccoli, money plant and wallflowers.
Look at the shape of the flower cluster to see if your "flower" is actually a group of tiny flowers. If it is flat on top, with each flower having a stem of a different length, a shape called an "umbel," chances are you have a member of the celery family, the Umbelliferae. These include many edibles, celery, astrantia and angelica among them, as well as the poisonous water hemlock.
Still haven't identified your plant? Many ornamentals have rather ordinary looking flowers, especially those in the rose family. Taking a specimen to your local nursery may be the best next step.