Rule #1: Warm up before you stretch. Stretching cold muscles is a good way to give yourself an injury.
You would probably become flexible more rapidly if you did Yoga, but I found that my muscles became much more flexible just from stretching after twice weekly exercise (I became able to actually touch my toes
).
There are a lot of standard stretches that can be found on the internet.
This page looks like a decent overview of lower body stretches. There's a more comprehensive overview, including muscle diagrams
here (don't let all the detail of this one put you off - you only need a small section of it. I recommend looking at the associated muscle pictures though, so you understand which part of your body a particular stretch is targeting).
Let your body be your guide. When you do a hamstring stretch you should feel the tension in your hamstring. Move into each stretch slowly. The muscle may be a bit tight and sore from exercise, but any sudden or stabbing pain is a sign to stop immediately. You can also feel which muscles are tightest as you stretch, so you know which to give most attention to - you may even want to revisit particularly stiff and sore muscles later in the day.