Why do it
Hill running is a form of interval training: it raises and lowers your heart rate in the same way that sprint training might do on flat ground. Incorporate this kind of training into your weekly routine and you'll soon see and feel the difference.
Not only will your lung capacity increase but your ligaments and tendons will get stronger from hill training. Your running form will also improve, because the uphill portion will not allow you to lengthen your stride, so forces you to adopt better technique. Do not lean forward or back; try to keep your effort level and breathing the same throughout.
How to do it
First, find a hill. Different hills have different effects. Long, slow inclines offer a good chance to dig in and test mental strength, while the sharper, more daunting peaks can help to increase power and strength. Hill training is not just for the confident and experienced, either. Beginners can power-walk up and stroll down, while those more accustomed to running can jog up and walk down. For advanced runners, sprinting up and jogging down should do the trick.