Any non runners just get up and run one day?

Yes.
I was never a runner and used to hate running when I was forced to run cross country during my high school times. Never run again after high school.
But now I enjoy it a lot.

A little less than 3 month ago, 2nd week of January 2013, I just suddenly decided to try out running (to improve my health) and have not stopped since.

My first day ran was 0.4 mile. And gradually improved within these 3 months. Now my longest is 7 miles and routinely run 3 - 4 miles almost everyday.

It's very important to learn how to run right. Otherwise injuries await you or you won't enjoy running.
Here is my little experience:
1. A good pair running shoes that fit your style. Preferably half size bigger.
2. Run at comfortable pace. Don't run too fast too far too soon. Don't let yourself run out of breathe. Slow down when it is about to happen. If you can find the right pace, you can run really long with that pace.
3. Go for distance first, do not worry about speed.
4. Land on middle of your foot.
5. Downhills can hurt your knee. Avoid them or don't go too fast.
6. keep yourself well hydrated before, during and after.
7. I used a heart rate monitor + cell phone app. Tracking heart rate allows you to pace yourself and compare results. It's really good as you know how well you perform and can slow down when working out too hard.

I do like the couch 2 5k program, thank you to all that recommended it. I am feeling some pain in my shins and my neck, which I thought was really odd because I've never had neck pain before, not even while doing insanity. Maybe I do just need different sneakers, right now I have the Nike Torch I think they're called. my shins still hurt and its been 2 days.

day 1 I did 1.86 miles
day 2 I did 2.12 miles - but not as fast.

My average pace has been about 10 minute per mile.

Oh and what do you know day 2 - 2 dogs chased me down the street I KNEW that was going to happen! The owner came running out and asked me to stop running so he could catch his dogs, I was not happy and a little bit terrified, they chased me right in the street. I'm glad none of us were hit =(

On the dog thing: look at that as a success because you met your fear head on, and everything was fine. I'm terrified of dogs when I'm out (I'm a speed walker considering running). Last month 2 dogs came running out at me, and I yelled for them to stop and go home. It freaking worked! =-O I was terrified to go by there the next day, but I kept telling myself that I won, and there's no need to be afraid. I've got to get some pepper spray one of these days.

Keep at it. You're doing great!

I did, I was living in a small town with not many gym / sport options but I wanted to get fit so I tried running. I'd hated running before that and it did take me a few months to consider myself 'a runner' but it's amazing how quickly you do improve. Start off with a mile and try to stretch it further each time. Go regularly and you'll be looking like a pro in no time.
Enjoy!

You could try one of these apps out there... the couch to 5K.

Personally, yes, I just threw on some shoes and started running and made it a point to run further each time. I also invested in a good heart rate monitor and like to keep my HR in a certain zone while I run. I can go months without running and then just go out and run several miles. Running isn't for everyone, and I don't love it like some people do, but in my eyes its the least amount of time to burn the most amount of calories for me.