I'll answer this in a couple of ways. First, I do not personally have much fear of injury. It's always a calculated risk, but with a lot of mitigation. You're at your greatest risk of injury when you are lifting in your 1-3 RM range, and when trying to push a new limit; and you're at risk if your form is poor.
Both come from bad lifting habits, usually developed early on. Poor form, with bench press for example, can involve things like bouncing the bar off of your chest. With dead lift, it might involve arching your lower back, and over extending. When I first started, these were pretty common mistakes. After a few times of having to "reset" my weight, and re-learn the lift, it was easier to get it right the first time - and I made all my errors when I was lifting light enough that I couldn't really injure myself unless I dropped the weight on my neck or something
I also had good role models. A few of my brothers had explored lifting already, so they kinda provided guidance along the way.
Lastly, I pay attention to my body. Learn to recognize muscular strain vs real pain. I know the difference between soreness and something which is bordering being injured - and if I'm hurting, I'll take a break. This is not "Monday is bench day regardless of what happens!" - It's a lifestyle I want to continue indefinitely. I lift so I can hike better and feel better.