Don't climb without a belayer . Always climb with one or more companions. If you are climbing with a rope, make sure at least one person knows correct belaying techniques to help you in case of a fall. The belayer is usually below the lead climber but may be stationed on top of the rock in some cases. Boulderers should always climb with a spotter.
Spotters help falling climbers land on their feet, using a pad to cushion the impact.
Do your homework. In addition to visiting an indoor gym and a sporting-goods store, read about the subject, talk to climbers and instructors, and take a few lessons. Then, do some additional climbing with experienced climbers. The best way to stay safe is to be well informed. Learn the lingo.