If someone is wanting to get into running or if someone has been a runner for a while, they should consider implementing some kind of strength training into their schedules for optimal performance as well as injury prevention. Running is already a taxing movement and puts constant stress on the body. This allows it to strengthen some areas of the body such as the spine, but if a runner does not take care of their body outside of running, or the only exercise they do is running, then injuries can arise. As a runner of 10 years, a competitive college runner, and now a personal trainer, there are three exercises/movements I encourage to be implemented into training.
Firstly, the running motion involves the entire body. With this being said, it is important to strengthen all of the limbs involved, and I like to isolate each limb. For example I like to do this by doing single leg squats, or bulgarian split squats. This will help develop power and strength in your quads, glutes, and even abdominals. For running I would keep weight light-medium and do about 10-15 reps on each leg. With running we want to focus more on muscular endurance. If your focus is more sprinting I would go medium to medium/heavy for about 6-8 reps to focus more on the power and strength of pushing through the movement. By doing single leg focused lower body movements, form will become increasingly important which will transfer over into running. To make this movement easier, you can work on just having one leg forward, the other back on the ground more so like a lunge, and can do this with only your body weight. To make this movement harder, put your back leg up on a bench to really work on depth, and this can be done with a barbell plus weight instead of only using the dumbbells.
Another exercise I would do for runners is some kind of row or lat pull down. I know that a lot of people do not think of running and think of a strong upper body, but I promise your arms, back, abs, can all fatigue out if you do not do some kind of strength training with them. I like single arm dumbbell rows because this will target the upper and lower back as well as stabilize your core, while providing work to strengthen your biceps as well. Your back and core as a runner play important parts to hold your form during a run. If you fatigue out in these areas, you will start swinging and crossing your arms expending unnecessary amounts of energy. Single arms dumbbell rows are also a fun lift to measure strength improvement and can be altered in a lot of ways to improve strength and stability.
Lastly, running is an easy sport to get overuse injuries such as shin splints, tendinitis, runners knee, etc. I would do some kind of banded knee ups, or step back to work on VMO strengthening. Doing rehab type work strengthens the joints, cartilage and tendons helping the stress put on the knees by running, preventing injuries and pain that will likely happen when doing the same motion over and over.