I run like a girl

One thing that I pay a lot of attention to when I'm running, is my breathing. Try to make sure you keep a nice rhythm. Don't strain yourself so much that you spend a lot of energy just to maintain your breathing. Keep a nice, cool pace to ensure you're breathing at a comfortable level. It'll probably help you run longer.

Running is really just about putting the time in. It is easier for some people in the beginning though. I would say give yourself a goal, like running 3 times a week for a month. Then see how you feel about it and if things are going well, create a more elaborate goal.

Your perception that it's a hard sport to segue into is not unique and not terribly far off the mark. The reality is that for every footstrike you're generating at least 3 times your body weight in impact force. It takes time for your body to adapt to this kind of stress. People characterize base jumping or skydiving as 'extreme' sports. But, for my money...running can easily fall into this category as well. It takes about 2-3 weeks of consistent training before your body really begins to adapt and it starts feeling more comfortable/natural. I'd agree with Ryan C's approach of 3 times/week for a month. I'd also say throw in some elliptical/stationary biking a couple times/week.