Dynamic stretching improves dynamic flexibility and is quite useful as part of your warm-up for an active or aerobic workout (such as a dance or martial-arts class).
According to Kurz, dynamic stretching exercises should be performed in sets of 8-12 repetitions:
Perform your exercises (leg raises, arm swings) in sets of eight to twelve repetitions. If after a few sets you feel tired -- stop. Tired muscles are less elastic, which causes a decrease in the amplitude of your movements. Do only the number of repetitions that you can do without decreasing your range of motion. More repetitions will only set the nervous regulation of the muscles' length at the level of these less than best repetitions and may cause you to lose some of your flexibility. What you repeat more times or with a greater effort will leave a deeper trace in your [kinesthetic] memory! After reaching the maximal range of motion in a joint in any direction of movement, you should not do many more repetitions of this movement in a given workout. Even if you can maintain a maximal range of motion over many repetitions, you will set an unnecessarily solid memory of the range of these movements. You will then have to overcome these memories in order to make further progress.
Ballistic Stretching
Ballistic stretching uses the momentum of a moving body or a limb in an attempt to force it beyond its normal range of motion. This is stretching, or "warming up", by bouncing into (or out of) a stretched position, using the stretched muscles as a spring, which pulls you out of the stretched position. (E.g. bouncing down repeatedly to touch your toes.) This type of stretching is not considered useful and can lead to injury. It does not allow your muscles to adjust to, and relax in, the stretched position. It may instead cause them to tighten up by repeatedly activating the stretch reflex.
Passive Stretching
A passive stretch is one where you assume a position and hold it with some other part of your body, or with the assistance of a partner or some other apparatus. For example, bringing your leg up high and then holding it there with your hand. The splits is an example of a passive stretch (in this case the floor is the "apparatus" that you use to maintain your extended position).
Slow, relaxed stretching is useful in relieving spasms in muscles that are healing after an injury. Obviously, you should check with your doctor first to see if it is okay to attempt to stretch the injured muscles.
Relaxed stretching is also very good for "cooling down" after a workout and helps reduce post-workout muscle fatigue, and soreness.
PNF
PNF stretching is a specific flexibility protocol that uses a combination of isometric contractions and partner-assisted stretching techniques. Several styles of PNF are used, the most practical being the CRAC (contract-relax, antagonist-contract) technique.
PNF stretching is best done with a partner after a light warm-up. A warm-up may consist of walking briskly, cycling for 5-10 minutes or engaging in any activity until you first break a sweat. Whenever you do a warm-up you are literally raising the temperature within the muscle. Warmer muscles make for more pliable, and therefore more injury-resistant, muscles.