What You Should Do and When
At first, I thought that a warmup should be a simple progression of whatever exercise you are doing. After much experience however, I have found that mapping out a good warmup routine is an integral part of any program. A great warmup routine can synergistically better your workout. Conversely, a poor warmup can negatively affect your workout and the results of your program. In much the same way a warmup gets you ready for exercise, a cool down can help your body gradually return to a resting state. Our body is always trying to achieve homeostasis and we can assist it after a workout by adding in a cool down.
First, when designing your warmup routine, its important for you to think 1 thing- "Gradual." In essence that's what a warmup should be; a gradual increase in readiness preparing you for a higher intensity activity. Your heart rate, body temperature, mobility, breathing, and alertness, etc... should all increase gradually to a heightened and ready state. In practice, start with simple and slower movements and work up to more complicated ones.
Not only should your warmup be gradual, it should also go from general to specific. In other words, it should start with the body as a whole and move towards the specific joints you will be using and movements that you will be doing. Starting out I have all of my athletes do a 2 minute "light jog" on their personal preference of cardio equipment. Rower, bike, treadmill, elliptical, stair stepper, etc... This accomplishes an increase in body temp, heart rate, alertness, nervous system readiness, overall joint mobility, and moves blood into the muscles. After their light jog the movements get more specific and target the body more discriminately.
Another important aspect of your warmup routine is to go from simple to dynamic. The first movements after the general portion of the warmup should be small, simple, and have a high degree of feedback. Simply put, feedback in relation to your warmup means more of your body on the ground. Think supine, prone, or all 4 limbs touching the ground. Then you should gradually progress to more complicated, larger movements, in a standing position. This allows your body to increase its proprioception
Lastly, a warmup should be focused on mobility first, then stability. Mobility is your active range of motion that you can control. Stability is the ability to create tension with your musculoskeletal system. Although it's not quite the same, stability can be seen as strength for this purpose. If our joints and tissues are not mobile, we cannot have stability. If we cannot get into a range of motion we will not know how to create tension in that range of motion. In this case, it helps us for our warmup to begin with exploring our mobility and move towards stability.
Think General then Specific
Think Simple then Dynamic
Think Mobility then Stability
Doing a quick cool down after some good training can allow our body to return to a more homeostatic state. It can be a good idea to increase mobility with foam rolling and static stretching. In fact, some evidence has shown doing these things post workout can decrease delayed onset muscles soreness (DOMS). Another good idea is to focus on breathing after your workout. There are many breathing exercises designed to calm the nervous system and even help your breathing muscles to work better. For a cool down it is easy to focus on breathing in through the nose and out through the mouth. Make sure the exhale takes longer than the inhale. For extra credit lay down on the ground and try to fill your belly up with as much air as you can as you breath in, seeing your midsection rise and fall with each breath. After an intense cardio session finishing up by going slow for a few minutes can help the body return to a more restful state. It can relieve the muscles and help get rid of metabolite accumulation resulting from intense exercise. Metabolite accumulation resutling from exercise is a good thing as it drives adaptation of our aerboic and anaerobic energy systems. Some light activity post-exercise can help shuttle it around to get used up and help your body recover.