The are just two ingredients to this success recipe.

Fix Your FORM-
You become lighter on your feet, then have a fluid stride, and get efficient and faster: it makes it all easier. Once you're an efficient runner, it all clicks. You can go longer and faster with less effort.

Be a HAPPY Runner-
Oh, such a cliche... but being a rounded individual will make your Running better. Talk to any accomplished or elite runners and they will talk about many other things that are not running too. Just like in running form, it’s all about balance: enjoy your sport but also don’t cut out the other things that make you happy.
Practice makes perfect. Check how you're sitting, right now. So, you're really good and sitting, and also hunching down?

Your body gets used to this and this becomes your normal. Your core gets week, your glutes disappear, etc. 
There's a German study that concludes that sitting is one of the worst things you can do for your health...

Get a standing desk if you can. For a stretch, I like to lower my desktop (I place it on a stool) and squat a few times a day for a bit. Or just get up and walk often, sit back, and make sure you do a few drills to straighten up before your run, or your all-day-slouchy-form will catch up with you, literally.
Arm movement is one of the most diverse variables in running form. There are not too many runners whose arm movements look alike. Unless we are talking about those people with perfect form.

Arms should be parallel to the body, bent at the elbow, hands pointing straight ahead, and your hip bone should get visits from your elbow and wrist.

No chicken wings, no hanging arms, no boxing arms, no arms crossing the belly button.

And keep in mind, the MOST IMPORTANT thing, is that whatever your arms are doing, your legs will do.

Pump your arms when going up a hill, your legs will shorten stride length. Relax your wrists, and your ankles will follow.

When you know your form is form is flailing, focus on the arms first.
Oh why oh why do people fight? Shod vs Barefoot, Barefoot vs Minimalist, Motion Control and Cushioned vs everything...

Really, all that matters is that you have proper form. Whatever you are running on. Yes, whatever.

Barefooters will tell you it's not possible. It is. I have video.

Shod Runners will tell you it's too hard to learn. It isn’t. I have video.

The "bigger" the shoe cage (less Proprioception), the harder it will be to learn to run efficiently. But, you can work (sometimes really hard) at it. It IS possible. Practice makes perfect, no matter the circumstances.
The three human forms of locomotion are:
- Walking
You "land" heel to the ball of the foot, with a push/strike of just 1 body weight for every step.
- Running
You land with the ball of the foot first and then put down the heel. Because of the swifter movement, you're now hitting the ground with two times your body weight. And because of this added weight on each footfall, you have to be careful and make sure you're doing this right.
- Sprinting
You land on the ball of the foot, and there is no heel touching. Now it's three times your body weight but it is faster so there is no time for the heel to come down and the elastic recoil takes care of the forward push.

All other combinations are just non-efficient mutations. Like the one where humans combine the heel to toe form (from walking) with two body weights (from running)... that's what Ron Burgundy would call "yogging". ;-)
My cadence in a 4 mile race this weekend. When I first checked my cadence, a couple of years ago, it was not higher than 140...
Have you heard of the 80/20 rule? It is the perfect way to describe Cadence and it's relation to Running Form.
Fix your Cadence and most of the issues you could have with your form will be adjusted. Not all, but most.

Cadence is your stride rate, and you should be doing anything over 180 steps per minute. 
Just as a test, go run for 10 seconds, count steps from both feet and multiple x 6.
You can also download a freemetronome app, set it up to 180 (or 90 if one foot at a time is easier) and compare to what you're doing.

Adjusting your cadence to 180 (or over) will shorten your stride length, help you land closer to your center of gravity, avoid the over-striding and heel-striking, etc. Cadence might just be the only one little-quick-fix-all.

Speed is about Power
Power comes from Efficiency
Efficient Running comes from Balance

Proper Running Form is all about positioning.
Running biomechanics are based on physics, place the right pressure on the right levers, at the right time, and you have efficient movement and power. It's all about balancing levers.

Huge quads, NOT what makes people fast.
Until you get your form analyzed, you really have no idea what you are doing.
We all think we run like Kenyans or Ethiopians that just need a little tweaking.
But until you see yourself in video, you really don't know.

That is why I like to start my coaching sessions asking clients to tell me what they think their form looks like. And then shock comes around. I even had the occassional kenyan get really upset when I showed him he was heel striking. The truth is, we all have a very romantic idea of what we look like. And it doesn't always pan out that way.
Make sure you get some video, and have an open mind about it.
It's better outside, the treadmill forces an un-natural gait.
Some running coaches will tell you to lean. Some running methods will also tell you to lean (chi-running, POSE method, etc.) Don't listen. They tell you that if you lean forward, your feet will catch your fall, and voila, that's running. They explain that "running is a constant fall". (And, seriously, is that what you want your running to feel like, like you are falling??? I want to FLY!) 
Leaning as a cue, does not work. People never do it right. They're supposed to lean at the ankles. And as hard as they try, everyone leans at the hip, or the waist. The posture breaks down, then they have to overstride to catch their "falling". That cue does not work. 
There IS a natural lean that happens when running, but do not try to lean. Leaning does NOT work as a posture cue.