I'd like to explain why I run and how not to think about it the wrong way (which, clearly, can ruin the experience). Perhaps you can make a similar case for any kind of workout, but certainly running stands out, at least to me, as a special kind of animal.
First of all, you can start for any reason. It is truly irrelevant why you start. I personally don't remember why I did, probably because I thought I needed to lose weight (wrongly so, 12 years ago I didn't have any extra weight and hardly have any now), and also because I remembered how poorly I did in highschool, not being able to last a minute. And so I started running. And at first it was really hard, running at 11km/h I could only last 5 minutes. Then somehow I made it to 10, then 20. Then finally I hit the magic number 30 minutes. I remember the day I first made it to 1 hour, it was a great feeling. From that day on I loved this idea that if someone's on a treadmill next to me, I'm not going to be the one going off it first.
Technique wise, I didn't always do it the right way though. I missed days, I ate before running, I hurt my feet so I couldn't walk - I made mistakes. But as in every other craft, those were necessary. I'm glad I didn't have a personal trainer or anything, that allowed me to calibrate my own body based on my experience (which is not to say I hadn't read anything on the subject).
But the most important part of running is not the how, but the why. The why, in my opinion, is quite fundamental and is shared by all runners: you run because it makes you feel great. Not at first, of course - for me it took years to get there. One of the obvious things is that you must do it every day, otherwise the joy and the magic evaporate. People intuitively think that routine makes up the worst of life experiences, but, in fact, it only depends on the kind of routine. Running to me is truly one of the happiest hours in my day, but it only is this way because I do it every day. Basically, it takes routine to get in the zone and then you can enjoy being in the zone.
A lot of people report being bored. I understand that, but I've never experienced that: doing the running routine is interesting, because it leaves space to daydream, but it's also interesting to push yourself, track your body's reaction, understand it better, understand when you need to stop or when you can push a little further. It's basically introspection.
A friend of mine recently suggested we do some biking in the nature: uphill, downhill, great work out. Needless to say, I sucked at it and I immediately felt how unprepared I was and how different of a workout biking was. But I had also thought biking doesn't allow for this deep introspection time running does, because you still need to watch the road, navigate the bike and the amount of mental energy spent on cruise control is certainly larger.
So I think you need to be the right kind of person for running, although since this is such a primal skill, I would imagine a lot of people are capable of doing it right. But the sooner you find the right reason to run, the better experience you will have. So my recipe is simple: don't do it to lose weight (in fact, you may hurt your knees if you have lots of that weight), don't do it because that's what others do at the gym. Do it for the sake of it. This will make you happy.
P.S. One of the best books on running that I read is called What I Talk About When I Talk About Running by Haruki Murakami. I've never read any of his fiction, but this one was a great biography full of amazing anecdotes and running tips.