This is one of those things I picked up when I was a teenager. It is particularly useful for hunters, but can be applied to many different circumstances. It is handy in physical sports, especially the outdoor sort. It can be crucial in self-defense situations, driving, and walking in crowds. It also helps to increase your observation skills and what you know about your immediate environment and the people in it.
Look straight in front of you. Tunnel vision is counter-productive, so don't stare. Raise the index fingers of both hands up beside your eyes and move them forward until they are just within your field of vision. Do not move your eyes to look at them. Rotate one hand up and down at the edge of your periphery vision. Do the same with the other. Get familiar with the extent of your periphery vision. Feel more than a little silly and hope no one sees you, you will look like an idiot.
Next, drop your hands and keep your eyes aimed straight ahead. Focus on the topmost point in your periphery, or 12 o'clock. Slowly, and without moving your eyes, shift your focus through the degrees until you come back to 12. Do it again in the opposite direction. If this is difficult at first, put a stationary object in front of you to look at and then focus your attention on something else within view without changing the position of your eyes. It its important to observe not just the edges of your periphery, but everything within your sight.
The eyes are drawn to movement. This is largely a function of periphery vision. By practicing and getting accustomed to utilizing your ability to scan your periphery without moving your eyes, you will become more adept at catching movement. You will also likely find that you remember more about an area after you have left it.
As with all things learned, it must be practiced until it becomes second nature. You know you've got it down when you realize that you start doing it without thinking about it.