I'm new to running as well and started off by walking...a lot. I trained and walked the 2006 breast cancer 3-day 60 mile walk. With my body used to all of the walking, I eased into running. In December '06 I started training to run a 5k in mid-Feb '07. Then in late March '07 I ran a 10k and in early May I'm running a 15k.
I follow Hal Higdon's training programs while preparing for races. http://www.halhigdon.com/
Hal has all sorts of training programs for all sorts of distances and multi-sport activities. You can also choose from the novice, intermediate or advanced levels (i.e. you can choose the novice 10k training program, or the intermediate 10k training program, etc.). I've been following the novice training programs and its working out well. I set goals for myself by registering in local road races that are progressively longer distances.
Based on my experience, here's my advice:
1. Buy a good pair of running shoes and socks from a real running store
2. Star sloooow. If you have to just walk for a few months, that's fine. You don't want to push yourself too hard and get an overuse injury.
3. When you're ready to start running, try the Couch Potato to 5K training program.
4. Once you've started your running program, register for a 5k that's a few months out
5. Buy some body glide. It's great for feet and other areas of your body that are prone to chafing. You can find this at the running store where you buy your shoes.
6. Stretch long and stretch often. I stretch before and after each run and do 90 minutes of yoga every other day. It makes a world of difference.
7. Hydrate. If you don't like carrying water with you on longer runs, drive your route and hide a water bottle or two along your route.
8. Wear suncreen always, and a hat if you feel you need it. A hat can help protect your hair from UV rays, shade your eyes from the sun and help keep sweat from running in your eyes. I wear a hat made by a company called Head Sweats. It's breathable, very absorbant and machine washable.
9. Cross train. If all you do is run you're setting yourself up for an injury. Swimming, biking, yoga, and even walking can compliment your running program.
10. Have fun!