1) You have a set number of exercises/reps that you have to complete and you try to finish them as quickly as you can. "Fran" is like this. So this might take you 12 minutes to finish, but it might take someone else 20 minutes to finish.
2) You will be given a certain number of exercises/reps that equal "one round." You will have to see how many rounds you can complete within 20 minutes.
I can't say that all crossfit gyms work this way, but at my gym (and I believe this is the norm) you will do a warm up that takes about 5 minutes, then you will do your workout (which generally lasts between 12-20 minutes), then you will roll around on the ground out of pain and dizziness for about 3-5 minutes, and then you go home.
One other thing... the first couple weeks that you do crossfit you will be extremely sore! Your body is going to need time to adjust to this level of exercise/stress. But within a couple weeks your body's recovery abilities will get much better. Just pop a bunch of Tylenol or Aleve the first week and don't give up!