Really just repeating what's been said above about starting out slow....
I've never been much of a runner. Way back in college I did some running, but at 18-19-20 years old you can do just about anything so running 5 miles was not a big deal. Around about 2008 I did some running but not a whole lot. Today I'm 48 y.o. 5'9". And 185 lbs on my way down to about 170 (198 on January 1).
For 2014, I made a resolution to be able to run a 5K because I found it a bit silly that I could ride a bike 100 miles but not run 3.1 miles. Last week I did a 7.3 mile run at 10:25 overall pace. About 2 weeks ago I did 5 miles at 9:46 pace. I've done several 10k runs now. In all cases, I felt no worse for wear the next day.
To get there in just over 2 months, I started out taking it easy. Partly due to the weather, I used a treadmill at the gym a couple days a week. Then I started running outside real easily. I followed the concept of couch-to-5k, but after two weeks I was already able to do more distance than what that prescribes. I think that's where all of the cycling came into play. But I still forced myself to do some walking in between running and would also do some light stretching after the walk-period before running again. And always stretch after a run.
I've also kept using the treadmill at least once a week. As someone without much of a running background, I think the treadmill allows me to move my legs faster and also run a higher heart-rate for longer periods. I'll probably phase that out now that there is enough daylight to run outside a couple days a week, but I think the treadmill was a big help.
I'm giving myself one more week of "just running". I'll start speed work, intervals, etc. the first week of April.