I agree there are different styles of riding as N NathanialStock said but I would not concern myself with all the minutia in the beginning. I learned to ride bareback on my own when I was a young child. No body taught me I was driven by a powerful desire to be up there. You can go pay for instructions which is probably the safest way to start but not necessarily the most exciting in my opinion.
Basically you have to seek the correct center of gravity in your seat and stay balanced during each gait of the horse. Of course walking is the easiest. Trotting is jarring and cantering is soothing and exhilarating. I loved the full out gallop when I was a kid. In all cases you have to be able to control the horse with the reins which are attached to the bit which is placed in the horses mouth and held on by the headset of the bridle. Most beginners will use the reins to "hang on" to the horse that is riding 101's biggest mistake. The horse will become confused about the message being sent through the reins if you are pulling to hard or jerking it about. The better trained the horse the more he will be confused because each different pressure on the bit means a certain command to that horse. A lesser trained horse will probably just get angry and may balk, buck or run away with you and try to get you off his back any way he can.
So riding is not just being able to stick on his back it which is important of course but you need to understand how to communicate with your hands, leg pressure and balance to let the horse know what is expected of him.
What is your motivation to ride ? As I said earlier mine derived from a deep desire to be one with the horse. It was organic if you will on my part. I embraced every aspect of the horse and his life. I got pleasure just from the smell of the horse, the feel of his coat and the rippling muscles.I would hop on his back out in the pasture, bareback, no bridle and sit while he grazed. I would spend hours "polishing" his coat until it gleamed. I would fall asleep on a bale of straw next to his stall comforted by his breathing and tail swishing and grinding his oats. Do you want to own a horse or just go experience a leisurely outing on a trail once in a while? I can tell you from experience that if you own a good horse he will teach you a lot. There are tons of books on the subject so if you are truly motivated get reading.
I could go on and on about this but I will stop here and see just what direction you are thinking of.