There are three basic types of stretching exercises that help accomplish these goals: static, dynamic and Isometric/PNF.
Static stretches are the most traditional type, encompassing the more or less standard 'pull to maximum end point, hold for five or ten seconds, then release' group of exercises.
Static stretches should form part of every 10 minute warm-up routine. Every major muscle group should be given a gentle pull, hold and relax. This helps improve the circulation and readies the muscles for more vigorous activity, while decreasing the risk of tears or tendon stretching.
Dynamic or ballistic stretches are more controversial, since they involve stretch with added momentum or even using weights. They are potentially harmful and that risk-factor is one of the major elements behind the controversy. At minimum, you should seek out a knowledgeable trainer before engaging in this form of flexibility training.
As one example, rest one knee on a ball and slowly rotate the ball away from the body, giving a very moderate bounce at the maximum point. Lunges, performed by moving one foot ahead, kneeling slightly with the back straight and bouncing gently, would be another.
PNF (Proprioceptive Neuromuscular Facilitation) involves a combination of passive and isometric exercise. Apart from having a fancy technical name and associated acronym, PNF actually has several useful features that should motivate individuals to investigate its value.
Performed properly, under the guidance of an experienced fitness professional or devoted amateur, PNF can maximize range of movement and best prepare the body for more strenuous exercise.
Several exercises involve using a partner. The muscle group you want to work is stretched under tension, then contracted for several seconds, and your partner applies resistance to inhibit movement.
For example, stretch your arms out and slowly move them behind you, then contract the biceps, triceps and shoulders. Have the partner gently pull your hands together a little past the 180 degree mark as you attempt to pull your arms back to 180 degrees.
As another example, lie on your back on a comfortable surface. Raise one leg vertically and have your partner grab your foot. Your partner then presses the foot gently backward until you feel tension on the hamstring (the muscle on the rear of your thigh). You then contract the muscles as you attempt to move your leg back down, with your partner resisting the movement.
These examples are to serve only to give a general idea of the exercises. PNF exercises should only be attempted after you have received proper, hands-on training. Done incorrectly they can lead to muscle sprain or joint damage.
Whatever your workout routine, be sure to precede it by good flexibility exercises. That will maximize your performance during the more strenuous part of the total workout.