Note: This article is not about stretching but is a summary of general rules to help make stretching more effective. I'll write an article about flexibility training in more detail soon.
Before discussing stretching let me first say that if you are stretching because of muscle pain then you do need to bear in mind that stretching alone is possibly not the answer. You may have to look at movement patterns, strength, posture, trigger point treatment, warmth, stress and tiredness among others. But if you have been given stretches to do, here's how to get the most from them.
Distinguish between "a few stretches" and a "flexibility session". Both have their place but achieve different things. A few stretches here and there can help prevent tightening up during a day at work, or after a training session. To improve flexibility most efficiently however it is best to have a regular flexibility session. This can be anywhere from twice a week to twice a day depending on the circumstance. Occasional stretches can be used between sessions to help prevent re-tightening. Bear in mind that it takes much more time and effort to improve flexibility than it does to maintain it.
About flexibility sessions. I use the title "flexibility session" here instead of "stretch session" because a flexibility session can include more than just stretches. They can generally last anywhere from 10-40 minutes. When doing a such a session take into account as much as possible from below but keep them fluid and varying. They should not be too rigid in structure... be flexible!
Don't launch into stretches cold. The body needs to be both warm and somewhat awake to get the most from stretches. Start with a few minutes of warm-up movements such as heel raises, standing rotations, shoulder rolls, hip circles, press-ups etc.
After a hard training session it's best to let muscles recover a bit, and refuel, before going into recovery stretches or a full session. Tired muscles are more likely to resist relaxing into stretch and are more likely to injure unless stretched very gently.
Mobility exercises, then dynamic stretches, then static stretches. If you are doing a flexibility session, any mobility exercises (such as shoulder rolls) and dynamic stretches (such as leg swings) should be done before the static stretches.
Keep still during static stretches. Keep still and focus on good stability and full body relaxation including the breathing. Think of relaxing into the stretch.
Volume is more important than intensity. It is generally better to have a longer flexibility session and keep the exercises less intense, than to have a short burst of very intense stretches. Violently tearing tissue is not a good way to lengthen it.
30s x 10. Static stretches of ~>30s duration for tissue lengthening tend to be most effective if repeated up to about 10 times.
Be regular. Tissue length does not increase overnight!
Avoid keeping the target muscles short for prolonged periods between stretch sessions. Move at least every half hour. Prolonged sitting is the enemy!
In warm-ups. Unless warming up for gymnastics, do not use static stretches in your warm-up. Leave static stretches for after, or in dedicated sessions.