The best stretch for your hamstrings is any stretch that you are comfortable enough with to do regularly. Regular stretching is the key to a longer, more flexible set of hamstrings, and the first key to achieving regularity is to find a stretch you like. Look for simplicity and ease of use. Far too often a person will attempt more than they are capable of when beginning an exercise regimen and end up disappointed with the results, or worse, injured. If you are unfamiliar with some of the stretches we mention, consider working out with a more experienced partner or putting yourself under the supervision of a trainer until you're comfortable with the exercises.
On Your Own
There are some hamstring exercises that can be done anytime, anywhere. If you're sitting down, try straightening your leg, pointing your toes up and out, and holding that position. If you feel a pull on the back of your knee, you're stretching the hamstring.
Using an elastic exercise band is helpful if you have very tight hamstrings. Lay down flat on your back and place a rolled up towel or small pillow under your back. Place the band around your foot, and lift your thigh up so that it forms a 90 degree angle with your torso. Pull back on the band, bringing your leg as close to your body as possible, and push your foot up through it, straightening your knee as much as possible. Hold it for 20 seconds. Repeat with the other leg. Try to do at least 10 reps.
An advantage to having a partner in your stretching is that you'll be able to go stretch farther, go deeper into the muscle and thus develop faster than you would on your own. One thing to remember is that partner stretches tend to be intermediate or advanced stretches. It is absolutely necessary that you move slowly and deliberately when stretching with a partner and to communicate with them in order to avoid overstretching.
A good starting partner hamstring stretch starts once again with you lying flat on your back. Your partner faces you and slowly lifts your leg up by the heel, keeping your knee straight, until you fell the stretch. Hold there for 20 seconds, and repeat with the other leg. 3 reps is a good target for this stretch.
A variant of this stretch can be done standing up, with your back flat against a wall. Lift a leg and have your partner catch it with a hand if you are not very flexible, in the crook of their arm if you can lift a little higher, or on their shoulder if you are flexible enough. Your partner lifts your leg until you feel a stretch, at which point you press down with your leg for 10 seconds. Your partner lifts your leg up slightly higher, and you press down, again for 10 seconds. Repeat three times for each leg.
Again, the best stretch for your hamstrings is the one that you will do. Find a stretch, and stick with it, and you will be pleased with the results.