Running is an excellent option for exercise and cardio vascular activity if you are looking to stay or get into shape, lose weight, and burn fat. It is also a great way to relieve stress and anxieties, and has been linked to many other mental health benefits including helping lessen depression and obsessive compulsive tendencies. How far you should run in a day depends on a lot of factors. You need to consider such factors as how much weight you want to lose and in what period of time you want to lose it in, how often you currently run and what your activity and exercise levels currently are (even if they are not just strictly running), and how fast you run or at what pace you run at.
How far you run each day and each week is different, though, than how many total steps you should take in a day. If you are trying to get more steps in overall, and incorporate exercise into your day on a more "global" scale (i.e. just trying to get more activity in throughout your day without going out of your way to have to bring your running shoes and get on a treadmill), then it makes sense to track your steps using an activity watch or activity monitor. A good rule of thumb, and one that a lot of folks are following these days, is to aim for 10,000 steps each day. That might seem like a lot, but little changes throughout your day can result in a big difference. For example, you can try simply taking the stairs instead of the escalator or elevator, and try parking farther away in the lot. Plus, getting up throughout the day and walking around your office building not only benefits calorie burn and fitness levels, but the mental break and stepping away from your computer screen can really improve your efficiency at work.
However, if you are trying to get more steps in your day just through running, then you need to really think about your current fitness levels, how much you are already moving, and what is a feasible amount of exercise to add to your routine. For instance, you don't want to try to up and start running 5 miles a day if you don't run at all. Start out with trying to walk/run two to three miles, a few days a week (in addition to what you are already doing). The benefit of running as far as calories burned and fat loss is that it more efficiently burns calories than walking - meaning less is more!