To reach 1st jhana, do we have to let go, or do we have to put some effort?
The method you cite first is correct.  Do not pursue the second.  Any authentic feelings of joy and rapture will arise of their own accord.  Anything forced or willfully attained is not jhana.  The first stirrings of jhana will invariably catch you by surprise and will seem to come out of no where.  We cannot force them to arrive.    

If I had to guess, I'd say the main reason why you [and really most people] aren't experience jhana is that you haven't been sitting enough.  Outside of a retreat setting, daily 90 minute sits is really the bare minimum for effective samatha meditation.  Any less than that and the mind just isn't quelled enough for jhana factors to present themselves in any kind of stable way.  To be terribly honest, you are also highly unlikely to find full absorption outside of a retreat setting.  It usually takes at least three days of 10+ hours a day of sitting for the mind to release its hold on the world and the grosser manifestations of the hindrances.  Only afterwards is the mind prepared for jhana practice.