Anyone can become a beekeeper. Urban beekeeping has experienced a resurgence since 2000, and more and more cities are agreeing that it's okay for people to keep hives in their backyards (though not all; it's still illegal in some cities). You’ll probably find more private backyard hives in cities like Portland and Eugene, Oregon; Boulder, Colorado; Madison, Wisconsin; and San Francisco, California.
But if it’s a professional beekeeper we’re talking about—someone who works for a company or starts up his or her own company, that's a bee of a different color.
You've got to learn about etymology (the study of insects, and of bees in particular)
Showing an interest in becoming an intern (paid or not, though of course, paid is always better) for a professional beekeeper or company that produces honey and keeps hives year-round is always a good option.