How can you properly warm up before practice or an athletic event? I am certainly not an expert on every sport, but I will give you some ideas on a couple sports that I do know.
In track you need to do some type of stretching for every area of the body. The old days of doing one lap around the track and then begin practicing will not work. Proper warm-up includes flexing the ankles, the knees, the hips, the elbows, the shoulders, etc. Every joint, and conversely every muscle attached to that joint, must be stretched and warmed up. To the passerby, a good track warm-up might look like a pre-school fun parade. The athletes are dipping down, seemingly falling forward, strutting, skipping & hopping, and the list goes on. Each one of these is done for a specific reason. During warm-ups they need to be watched by the coach or the young athletes will actually not be doing much more than the pre-school people mentioned earlier.
When you go to a basketball game, what does the warm-up there consist of? You have lay-up drills, shooting drills, free throw drills, cutting drills, and so on. Each are designed to simulate what is going to happen in the game. All other sports have their own specific warm-up techniques.
On the warm-down side, these drills are designed to get the body’s muscles back into a relaxed state before you sit down and have the blood flow concentrate in the wrong areas. I am not a doctor, so I will not pretend I know all the physiological reasons for this. I think you get the idea.