1. Stretching most definitely will improve your flexibility, no matter how fossil-like you think you are...
2. Most people recommend stretching a minimum 2-3 days a week. But the higher your weekly frequency the faster you will see improvement of range of motion... Like 4-5 days a week. And like someone else said, hold it for at least 20 seconds.
3. Don't do anything that hurts acutely. I would try and avoid anything that twists your knee (ie. hurdlers stretch) or hips in an awkward way...
A kinesiology professor I had a few years ago claimed there were only 3 stretches you ever had to do... Still not sure if I agree with that, but they are all good stretches.
1 - Sitting V-stretch. Perhaps the most common stretch ever? Sit with your legs in a v, lean your body forwards trying to keep your back flat.
2 - Hip flexor stretch. Lunge forward with one leg, keeping your body upright. Your front knee should not extend over your toes. Lunge lower till you feel a strech on the hip of the back leg.
3 - Shoulder flexor stretch. Sit on the floor with your legs straight out in front of you arms at your sides. keep walking your hands farther behind you and closer to eachother until you feel a stretch in your shoulders...
Happy Stretching!!!!
ps - I like yoga better than stretching... try it out!