The Squat

When you squat the only thing you do is squat.

The Setup:

Your foot position on the squat depends on your personal preferences although I do not think that pointing your feet inwards is a good idea.
Start with your feet pointed forward and parallel and squat down without a weight.
Move your toes slightly outwards repeat and adjust where you feel until you reached your most comfortable foot position.
Your feet should be rooted in the floor during the squat.
The cue "Push your knees out" in my opinion is not good due to the fact that if you exaggerate on pushing your knees out you will lose stability just as well when your knees cave inwards.
Therefore I think it is best to have your knees be in line with your feet and not have any unnecessary movement during the squat.
But the squat is an exercise where knee flexion/extension occurs but not more and not less.
A common mistake people make when they squat is that the flexion of the hips occurs through the lowering of the upper body instead of "dropping" their hips and glutes into the bottom position aka the "hole".
Mark Rippetoe tells male youngsters,"I want you to drop your dick in between your legs."
So basically you drop your pelvis in the hole which means flexion of the knees, flexion of the hips, eccentric contraction ofthe glutes and an isometric contraction of the quads[these are the prime movers, IMO].
 Your upper body is tight all the time especially your back which of course is balanced by your abdominal wall which is tight as well.
The position of the barbell on your back is dependant on you and where you feel the most comfortable but I would not put it directly on my neck or wrap a towel around it for that matter.
Towels are only useful for watery hypoosmotic secretions of your skin.
Hand placement depends on your flexibility[mostly shoulder] but the closer you grip the more pressure is being put on the elbow but it helped me create more tension in the upper back.
So once again grip where you want and are painfree.
A close grip also forced over-extension on my wirsts which I balanced with wrist wraps but it only happens with heavy weights.
Head position should be looking straight forward or slightly upwards. Looking down can cause rounding and therefore loss of tension in the upper back and is basically asking for injury on heavy weights.

The Squat:

Grip the barbell tight.
Get under the barbell and place it on your back.
Get your whole body tight and unrack the barbell.
Walk back so that you have free space to squat.
Adjust foot position if neccessary.
Get a deep breath of air and hold it.
Whole body tension.
Squat down in a controlled manner.
When you reach the hole [do not round your lower back! keep it tight] squat up.
Squat up with maximum force but be in control of your movement.
Do not explode up since you want to squat and not jump.
Do not fully extend your knees.
Repeat as many times as possible.
[A good indicator of form is upper body tension.]