A very good rule of thumb is that for any exercise is that if it doesn't aggravate your symptoms, you can do it. In your case, if running doesn't make the radiating pain worse, go ahead.
There are various beginners' running programmes out there (people mentioned C25K). Any one of those will do. Or you can just wing it. When you start off running, the idea is to build up your ability to accumulate "easy miles"- distance covered that doesn't tire you out much or get your HR up too much. That kind of running builds your aerobic capacity and also makes a lot of the changes that your body needs so you can run well. When you are doing easy miles, you have to check your ego at the door- if a 50 year old man or two attractive college students blaze past you in the park, you stick to your guns, just keep gently plodding away at your unathletic-seeming pace.
So, in terms of progamming, what you do is gradually increase both distance/time and frequency. When you start out, you might just do it twice a week for fifteen minutes. A week or two later you might do it twice a week for twenty minutes. Your general target is to get the time up to 40-60 minutes (the period of time some people think is ideal for getting positive changes to your heart). You can also gradually add days- start off doing it twice a week, and once you are feeling good do it three times a week, then four times a week.
IMO, you want to build up to doing 25-40km a week (e.g. 4 runs of 8-10km each), all at the "easy miles" pace. You may need to run for longer than an hour sometimes in order to hit your distance targets. And once you can handle that without ever being tired or stiff, you need to keep that up for a 2-3 months.
This will in no way make you a good runner, but it will mean that you can run recreationally, and also allow you to train more seriously if you want to. A bit of speed work, threshold training and some practice 5ks and you'll probably have an okay-ish 5k time. Or you can further increase your mileage and train for longer distances. In either case, you will have the basic aerobic capacity and physical readiness to take on harder training without hurting yourself.