Warm up and cool down. The most important things to keep healthy and reduce injury.
Warming up before practise and before dance is one of the most important elements of dancing safely. Especially in the cooler months of the northern hemisphere at this time of the year. These are a few pointers I have gleaned for you. Please comment and add your own suggestions to these pointers.
Some dancers may stretch improperly at times, and while doing so may not affect them immediately, but eventually can, causing serious injuries that may affect their dance career in the future.

Stretching properly before dance is very important for strengthening your muscles, increasing flexibility, and making your moves flow more easily and gracefully. Stretching is the best warmup for dance, and it helps dancers to leap higher, do the splits, turn faster, and have more focus. In this article, you'll find many helpful tips on how to stretch properly before dancing.
• Get the right gear. You will need comfortable clothes, such as a t-shirt or tank top and dance shorts with tights, jazz pants, or sweat pants. If it's cold, wear a comfortable sweater. Make sure you can move your body in these clothes and that they aren't too small.
• For the gear, it's good to have a yoga mat, a big yoga stretching ball, and a nice, wide space to stretch. Have a bottle of water near and a snack for after you stretch.
• Begin stretching. The first stretch is aimed at engaging your hamstrings and increasing flexibility. It is good for jazz and modern dance
• Lay down on your yoga mat, one knee up. Make sure your hips stay planted on the ground.
Slowly and carefully pull your leg in the air, holding your leg completely straight, toes pointed. Do not hold your leg with your hands behind the knee, as this causes an injury to the hamstring. 
Depending on your flexibility level, either hold your leg behind your thigh, or your shin, which takes some skill in flexibility. 
Hold your leg there for two sets of eight counts, not bending your knee at all.
Slowly, pull your leg back in, holding the knee for eight counts. With that same leg, hold your leg out beside you, like you are doing a sort of straddle split with one leg. Again, do not hold behind your knee. 
Pull down your leg as far as it will go. Hold this position for eight counts, and slowly bring your leg back in for four counts.
Repeat this whole stretch with your other leg and then do it again with both legs at the same time. This stretch takes up to 10 minutes to perform if you do it completely.. 
• Proceed to the next stretch. Stretch two focuses on increasing flexibility and stretching your shoulders and abs. It is good for ballet and jazz dance
• Sit in your butterfly position, with your legs held attitude (bent), your feet facing each other, like a mirror.
Slowly, holding your feet, drop your head –hands touching your feet, and hold for two sets of eight counts.
Rise up, contract your back, and dropping your head again, and hold.
Do this stretch five times, contracting your back before you drop. This stretch should only take 1 minute or less to perform.
• Do the next stretch. Stretch three focuses on increasing flexibility and engaging hamstrings. It is good for Reels and Jigs
• Sit up straight, with your legs also straight directly in front of you, coming right out of your hips.
Flex your feet, grab the arch of your foot, put your head down, and hold for eight counts. If you cannot reach your toes, go as far as you can, keeping your head down.
Rise up, and sit in your straddle position, similar to Stretch One, only sitting up and with both legs.
Choose a leg, and bend to touch your toes, flexing your feet. As log as you are reasonably fit then you should be able to touch your toes. 
Point your feet and rest your head on your knee while stretching your other arm touching the back of your other hand.
Repeat the previous action with your other leg.
Shake your legs when finished to release tension. This stretch should take no more than about 4 minutes.
With both arms stretched in front of you, bend down, letting your arms brush against your toes.
Hold this position for two sets of eight counts.
Then, next, reach down, putting your hands on the ground between your feet. Hold for a few seconds.
After that, stretch your arms, behind your back. Using your right hand hold your elbow and pull it in the direction of the other side (for example, the left arm is bent behind your back, the right hand pulling to the right).
Hold for a count of 10 and then change hands and stretch to the opposite side. Repeat for about 2 or 3 minutes. 
• Move to the next stretch. This stretch aims to loosen your neck and help you relax It gets you to focus your energy while also stretching your neck, a must for any type of dance
• Sitting down, bring the soles of your feet together and open your legs with your hands down by your sides
• Slowly, to a regular count/ beat, shake your head from side to side Do this for eight counts.
• Then, start nodding (up and down) for eight counts.
• Roll your head slowly, -do not do this vigorously-keep it slow. Roll the other way. This should take about 2-3 minutes at the very most.

Work on your splits. Now that you have stretched your arms, legs, and your back, it's time for the splits. Get on one knee, and slowly straighten both of your legs. With one hand on either side, slowly and carefully slide all the way down, as far as you can go, and hold for as long as you can go. Repeat this procedure with the other leg. For a straddle split, sit in your wide straddle and lift up. Make sure that you toes are pointed the whole time. Just take as long as you need. This is a must for any type of dance, as you need to stretch your legs, always!
Add a little agility. This may seem harsh, but it strengthens your core and helps to make you stronger for dance. Every day, even when you don't dance, do 15-20 sit-ups, 10 pushups, 5 pull-ups, and run when you have the chance. If you can, try to do half a mile a week at the very least. Take as long as you need. This step is vital for any dancer who wants to improve.
• Push yourself. Tell yourself, "I can do it! Full out! 8 more!" It will make you a stronger dancer mentally and physically.
• Stretch every time before dance, as you will be warmed up and have a less risk of injury.
• Remember to thoroughly breathe during stretches. Holding your breath during a stretch will not help your body to relax.
• Use proper dance shoes or barefoot. Not sneakers.
• If your teacher has any specific stretches he/she does/doesn't want you to do, always follow their instructions before referring to this article only.
• Stretch with a friend. You will widen your range of stretching options.
• All of these stretches are safe to do for dance; do not worry about breaking your legs or pulling a muscle. Although, the splits can injure you if you go too far out of your comfort zone, so don't get too ahead of yourself.
• Practice backbends/bridges on a large yoga / exercise ball.
• Listen to what your teacher tells you; they are professionals and will give you the best advice.
• Do not do stretches you are unsure about because this could cause risk of injury.
• Interestingly, you could add a different discipline to your warm ups such as Yoga You can get a yoga book or DVD to help you.

Cooling Down After Your Workout
• When you are ready to wrap up your workout, it is sometimes tempting to just finish up and possibly hit the shower. Once your heart rate is up and your muscles have been taxed, this is an important time to give your body a chance to cool down. If you have just completed a strenuous dance session, for example, take this time to work out slower .Keep your body moving so that your heart rate can gradually resume its resting rate.
• The cool down portion of your workout is also an important time to stretch your muscles. Your muscles are at their warmest during this time, which makes it the perfect time to deepen your stretch. Take the time to stretch each muscle group that you exercised. Breathe deeply through the cool down period to help your muscles melt into the stretch. You will find when you stretch during the cool down that you will feel less soreness from your workout. Besides helping to prevent injuries, this decrease in soreness is important for maintaining your motivation to adhere to your workout routine day in and day out.

Other articles on warm up and cool down.
"IMPORTANCE OF A SPORTS WARM-UP AND STRETCHING"

Warm-up is one of the most important elements of an exercise program. It is particularly important to prevent injury: 
Warm-up is low level activity, such as a brisk walk or a slow jog, which should be completed prior to stretching and more strenuous exercise. The objective of the warm-up is to raise total body temperature and muscle temperature to prepare the entire body for vigorous activity. The warm-up period prepares the cardiovascular system, respiratory system, nervous system and the musculoskeletal system by gradually increasing the demand on those systems so that they are able to accommodate the demands of more strenuous activity. 

Passive Warm-up:
The main goal of passive warm-up is to increase body temperature, either total body temperature or local body temperature, without physical activity. In passive warm-up the body temperature is usually increased by some external means, such as wearing heavy apparel, like a sweatshirt, and/or a massage with a topical exercise rub, such as Ben-Gay. One of the advantages of using a passive means of warm-up is that energy is not expended in the warm-up activity. However, for best results it's recommended that passive warm-up be used in combination with active warm-up.

Active warm-up:
Is composed of two types: general and sports specific warm-up. The general or non-specific warm-up utilizes low intensity movements such as walking or slow jogging general warm-up, involving low level activity, is usually more effective than passive warm-up in increasing deep muscle temperature. Specific warm-up exercises actually involve the body parts that will be used in the subsequent competitive event. An example would be swinging a tennis racket in a practice stroke.
The advantage of the specific warm-up is that the temperature is more effectively increased in the specific body parts that are to be used. 

THE PURPOSE OF WARM-UP: PREVENT INJURY - ENHANCE PERFORMANCE 
Experts agree that the main purpose of warm-up is to increase the blood circulation in order to raise both the general body and the deep muscle temperatures, which in turn help to heat up the muscles, ligaments and tendons in preparation for more vigorous activity.
A proper warm-up provide many benefits due to elevated temperatures associated with it. The likelihood of injury is reduced. Athletic performance can be improved. The warm-up increases muscle efficiency, reduces potential for muscle pulls, improves reaction time and improves the speed of movement of muscled and ligaments. 
Proper warm-up can also help reduce the severity of post-exercise muscle soreness. The higher temperatures and increased blood flow resulting from warm-up are important for delivery of oxygen to the muscles and for prevention of build-up of unwanted waste products which can lead to muscle soreness. 

INTENSITY and DURATION of WARM-UP 

It is difficult to recommend specific intensity and duration of warm-up for every person, but most research in this area suggests an increase in body and muscle temperature of approximately one to two degrees Fahrenheit to be adequate. A brisk 5-8 minute walk or a slow jog will generally produce sufficient warm-up to prepare the body for more strenuous exercise. 
The duration and intensity of warm-up should be adjusted according to the environmental temperature and the amount of clothing worn. The higher the environmental temperature and the greater the amount of clothing, the sooner the desired body temperature is attained. It is also important to begin a major activity while still warmed-up. Ideally, the rest period should be more than a few minutes. In any case, no more than fifteen minutes should elapse. When the beneficial effect of warm-up has dissipated, the muscle temperature will have returned to pre-warm-up levels. 

THE DIFFERENCE BETWEEN WARM-UP and STRETCHING: WARM-UP THEN STRETCH 

There is an important difference between warm-up and stretching. Many people stretch and call it warm-up. This is incorrect. It is important to warm-up before stretching. If one stretches the muscles without prior warm-up, the muscles are cold and are more prone to injury, such as muscle tear or strain. Before exercising, begin with a warm-up period to raise the temperature of your body

You want to get the heart pumping and increase blood flow to the muscles before stretching. Slow running in place, a slow aerobic dance, or a walk-jog (all with ball), and the application of an external exercise rub, is an ideal warm-up regimen to help prepare the muscles for stretching.
This was extracted from an article by Ahmad Tousi, FIFA Licensed Coach