I have spoke with many beginners, and not many of them have failed on this program. This may be too easy for some who are already fit from other sports. If that is the case, you will have to assess your own individual needs. I cannot generalise with any degree of accuracy where you can start, but what I can say is, everyone could start here. With the "Couch-to-5k-Running Program".
All the information you need is here.

If you feel that this plan isn't for you, then you may wish to take a look here. I have also listed some programs for 'advanced' beginners. These would be helpful to those people who are taking up running but are fit from other sports.

• Runner's World - 5k Plan
• About.Com - 5k Plan
• Running Times - 10k Plan