Find a local archery shop, or sporting goods shop that sells archery equipment. Talk to someone knowledgeable about archery and equipment. Buy something economical but of good quality, get some lessons if necessary, find a safe and legal place to practice, and shoot away.
I suggest you stay away from compound bows. Get a good long bow or recurve and shoot with that. It's a more natural, instinct method, whereas the compound bows can be outfitted with all kinds of sights and counterbalances and whatnot that make them very accurate, but they become more like an arrow launching machine, and less like traditional archery.
Historically, many many (most) cultures around the world had archery of some kind or other. There were differences between them, but the similarties are probably greater. So if this isn't "ninja style" archery, it is still simple, traditional, instinct shooting archery, and it's a good and fun thing to do. So go ahead and add it to your repertoire.