There are two different ways to go rock climbing, expert?s call then aid climbing and the other is free climbing. They are exactly as they sound. Some people like the experience of rock climbing but they want to go with someone who knows how, with aid climbing there is a sense of safety. Then there are people who like to go free climbing this is unassisted rock climbing.
More technical, aid climbing is climbing rocks with artificial instruments that are put in the rock and can be used as foot or hand holds so you have something to climb on as you scale the wall.
Free climbing is having the climber use nothing but their hands and feet no other aids. There are different categories of free climbing, the traditional lead climb, the leader of the climb can use the devices that aid climbers use to scale the wall. It is basically a follow the leader game on a rock.
Sport lead climbing uses pre placed bolts that you climb on for protection. The act is supposed to let the leader talk off his gear because he has the protection of the bolts. You should never remove the gear you have without; you never know when you may need it.
Top rope climbing or top roping uses a rope that is hung from an anchor that is put into a rock on top of the rock. The climber uses the rope as a guide that allows him to climb faster and more accurately.
Then there is something called bouldering, this is climbing on severe dangerous boulders that are usually on bad terrain. There are safety ropes available but the people who prefer the use of mats to land on. Free solo climbing is climbing without anyone to help you or guide you.
The safest way to rock climb is to go the indoor rock climbing but if you feel the need to experience the rock climb then make sure you do it responsibly and safely.