Flexibility, and attaining a greater degree thereof, strikes me as being very similar to bodybuilding: you need a set of basic movements, the knowledge to do them correctly (and not get hurt), and the discipline to perform them regularly. If your hapkido school is good, the instructor will be qualified to be your main source of help. Ask him/her to teach you some stretches that you can perform every morning. A lot of martial artists espouse the benefits of splitting stretching routines throughout the day, e.g. static stretches for 15 minutes in the morning and then 15 minutes of dynamic stretches in the afternoon.
So, to answer your question, some stretches may require a set & rep scheme, like 'hold this position for 60 seconds each for 4 reps'. That's what you should ask your instructor or what you should look for in further reading.
Here's a good overview of stretching and the types of stretches available (static, active, dynamic, isometric, etc):
Stretching and Flexibility - Introduction
I actually purchased this guy's flexibility book. He seems to have a good idea on how to progress from 'little' to 'lots'. He also has some good ideas on bodyweight exercises. I'm not trying to hawk his warez, but this might be worth checking out:
Get Full Splits with Stretching Techniques Proven to Increase Flexibility and build Strength!