First thing is to hydrate yourself appropriately at all times. And get yourself some decent running shoes.
I advise to draft a schedule and stick to it. The first 4 weeks are the crucial ones as you will develop your habits and expand your stamina.
The first day, I would go out and run for 1 minute and walk 2. Repeat until you hit your distance goal (probably about 2 miles in 30 minutes at that pace).
Second day, I would just walk, regardless of how you feel. No matter your health and shape, if you haven't been running consistently, it can be tough on your body to begin a running program.
For the rest of the week, rotate between the first and second day's exercises.
Each week, continue to increase the ratio of run vs walk on your run days. I would recommend going to 3/2 next, but really, it's up to you. If you push yourself too hard, the likelihood that you won't stay with it is astronomical due to a variety of reasons.
Keep your calcium intake high as well to keep your bones strong. It is common to get shin splints or sore ankles/knees in the first few months but that will go away.