There are a lot of ways to teach people how to squat. These include books, DVDs, articles, and videos.
Here is another one.
Most of the articles and videos start from similar point - start from standing, squat down, stand back up.
However, not everyone has the strength, balance, and body awareness to successfully and safely squat down and come back up. The body awareness is especially difficult for new trainees - they can't feel what is a correct squat or correct depth.
First, figure out where the bottom is. Tony Gentilcore's article, linked yesterday, is a great place to start. First identify how deep you can go.
A quick substitute, is to simply sit on a bench or box that puts you at the same height you would be on a chair or sofa at home. It's practical alternative since you will need to get up from that height as part of daily life.
Next, start at the bottom. Almost everyone can sit down. Start from the box/bench/chair. Get down however you need to. From there, you can get your feet placement the proper width for a squat, tighten up your hips and abs, put your chest up, and drive your feet down and stand up.
Really, all a squat is, is standing up. You do it under a load, and you generally start and end standing, but you're standing up.
Your goal is to get with without having to use your hands, grab onto anything, shift your weight to one side, or push off your legs with your arms. If you have to, do it as little as possible. Try to increase the number of reps you can get without assistance.
What are the upsides to this approach?
You take away any fear of falling which commonly cuts squat depth and discourages people from sitting back into the squat.
You can adjust the bottom position without being under a load. You can correct chest position, foot position, starting motion, etc. at the most critical point in the squat - the bottom aka the hole. That is where your barbell back squat will either succeed or fail, so you can get it right first.
You can do this with even extremely de-trained clients. Even the most elderly client will sit down and get back up during the day, and if you can get them doing it without any assistance you are given them their life back. If they fail to get up due to fatigue or old injuries creeping back, you can stop the set with ease.
It will also result in less soreness, since the motion is all concentric (muscles contracting/shortening), not eccentric (muscle lengthening.)
It's easy to get used to what a squat depth feels like.
Almost no one gets up on their toes when they stand from a chair - they drive with their heels and keep their feet flat.
It's easy - and safe - to put a band around the knees to force the squatter to push their knees out.
Progression - how do you progress these?
Move up to goblet squats.
Add a weight vest.
Use a lower box (great in conjunction with mobility drills to increase range of motion). Whenever you do this, start unweighted in case the person can't keep a proper back arch in this position.
Work up to a barbell.
Start doing single-leg squats (lift one leg and stand).
I find this approach very simple and easy - young and fit people can move right up to the bar the same session; older and injured people can stay at this until they build up the strength to progress to the bar. Plus it's safe, intuitive, and it's clear when progress is made - if you can go from "stand up with a cane or using your hands" to "stand up unassisted, with a load" you know you have made progress.