I used to trail run on singletrack that I found to be fairly challenging on a mountain bike, about a 7 minute drive from my house. It was a good 4 mile loop or so around a reservoir, and boy what a workout that was if I did it in under an hour. Had lots of short, steep hills...
Get sneakers specific to trail running for it. They are not as cushioned as road sneakers and give more stability and traction. Go to a running specialty store, too (not Footlocker or anything like that) so you can get properly fitted.