Let's face it, running puts a lot of stress on your body. Not that it's the exclusive means to do so. I've sprained my ankle at least 6 times, and only once was running. The other 3 times I was merely walking - another very dangerous activity.
I'm not a doctor, and I'm by no means trained to give any sort of medical advice, but I'm happy to share with you some of my tips and trips for the common running injuries I've experienced.
My first piece of advice? See a doctor. Not for everything. I mean, if you fall in the middle of the intersection and scrape your knee (been there!) you're probably fine. But pain in your back, hip, knees, go get checked out. At the very least it will get you some physical therapy - and I swear by physical therapy for runners. Because PT gives you exercises to help strengthen whatever injured body part you have, so you don't continue to injure it with repetitive movement like running.
Secondly, invest in a foam roller. Based on absolutely no empirical data I will say a majority of problems from running comes from muscles that are too tight. These tight muscles, located in places that are difficult to stretch, like your piriformis, in turn affect the surrounding muscles, tendons, joints, ligaments. Rolling out the muscles (myofascial release) helps to break down the tightness in these muscles. It hurts. If it doesn't, you're probably doing it wrong. But regular rolling helps to prevent future injuries.
My third piece of advice is also preventative. Get fitted for running shoes. And then, find the right running shoes for you. So many issues are caused by bad, old, or ill fitting shoes. But you need something that's going to support your running, not hinder it. When I first started running seriously I was fitted and recommended a pair of New Balance. My first run in them gave me my first ever shin splints. And knee soreness. They went right back. Even though they were the "right shoe" for me based on gait, they didn't work well for me. I typically wear neutral shoes, and find Nikes to be a good fit for my long narrow feet, but even within the Nike brand, not every model works for me. So it's a trial and error process, but in the long run, your body will thank you.
Most of my injuries have involved my back - slipped discs and SI Joint dysfunction. And although running has never been the cause, it certainly can aggravate injuries. My fourth recommendation, is to be realistic in taking stock of your body. LISTEN TO YOUR BODY. I was once in the middle of a 10k when I almost broke down crying because I was dumb enough to try running it with a disc problem. Dumb. Dumb. Dumb. And a surefire way to ensure you're running shoes are packed away for an even longer time. Back and knee issues are nothing to mess with. And sometimes that means you need to rest and treat instead of pushing forward.
My other running injuries have centered around my IT band. Which is where I discovered the wonder that is KT Tape.