In my opinion, as a runner you primarily should do squats for mobility first and strength second. Strength gained from squats probably won't help your running training. HOWEVER, using squats to increase mobility and work through all of the muscular imbalances that you develop while running, that is something different.
So here is my simple guide to beginning to squat, with a focus on mobility first.
Question #1. Can you do this?
If you can sit in this position, can you do it for 10 minutes? In my opinion, if you can't mobility is more important for you than leg strength. Odds are that you can't get in this position and definitely can't hold it (I sure as hell couldn't 6 months ago). That is a function of being older than 40, having a "desk jockey" job and heavy travel schedule (lots of sitting), and doing a ton of running. Tight hips, hamstrings, etc, etc.
When you get up from a squat position, do you look like this (i.e. shins vertical, lift with your hips)?
So the goal is to squat like a 3 year old. Simple.
The first thing to do is spend a bunch of time each day in the bottom squat position. To figure out how that position should look, work on a goblet squat. Read this article to learn more about the goblet squat. Ignore the pictures in the article about doing it with two kettlebells. Do goblet squats holding one dumbbell, or with no weight and just use your elbows to shove your knees out. This article has less background information and more instruction.
Dan John invented the goblet squat. If you want even more info, google him and you will learn a ton of stuff. If you have 50 minutes to kill, this video of a Dan John seminar is the clearest and best explanation I have ever seen on the basics of squatting:
As a runner, I would argue that you should only goblet squat until you are so flexible that it is as easy as brushing your teeth. Don't worry, done even modestly correctly, the goblet squat should fix all of your back concerns that stem from regular squatting. Once you work up to being able to do sets of goblet squats with a 50lb dumbbell, then worry about heavier back squats, etc.
Then you can do front squats like this:
Or back squats like this: