If your son is new to the sport of running, then avoiding injury begins with starting low and slow. One of the most common ways runners (especially new runners) get injured is that they push themselves too hard, too fast. It is understandable, especially if your son is running in a group, club, or just with others, that he would want to quickly get better at running to keep up with the others and be able to participate in all the group runs and workouts. But running is hard! It can really take a toll on the body to push it to its physical limits without having first built up a solid running base.

Another extremely common reason runners get injured is from overuse injuries, meaning they are running too often for their bodies and are not taking adequate rest days. If your son wants to start running, encourage him to do so! But also make sure he is not running more than once a day or consecutive days in a row, especially at first. And emphasize proper recovery. This does not stop at just getting enough sleep and taking days off, but nutrition, stretching, and even light weight training play into helping the body recover well to avoid injury. He needs to be eating a lot of protein to rebuild his fatigued muscles, carbs to fuel his runs, and fats to promote hormonal health and proper functioning of many of the body's different systems. And make sure he is warming up and cooling down before every run. Stress to him the importance of the warm up in particular, as going out and running on "cold" muscles can be a recipe for disaster.

Finally, if something starts to hurt, immediately stop. Runners tend to be a very Type-A, hard headed bunch of folks. Which means they can push themselves through tough workouts and race conditions, but also means they might push themselves physically farther than they should, to the point of risking an injury. It's not worth it! Don't take chances with health and well-being. If something starts to hurt, stop and take some time off. And if it continues to hurt even after resting and icing, see a doctor.

Sources:
http://kidshealth.org/en/kids/sport-safety.html
https://www.active.com/fitness/articles/how-to-prevent-injuries-during-exercise