In few days, I will become a father and I was wondering how to say adhan in the right way? As new baby has a very delicate ear, so does one whisper, or say it out loud but from a distance? Should it be in both ear or just one? Who should be present at the time of adhan?
It is not necessarily to be a quiet whisper, but it has to be recited through the right ear. And when you're done with adhan, recite the iqama through the baby's left ear.
However, all hadeeths that talked about this matter are considered da'eef (weak), especially the part of iqama. See this https://youtu.be/vXD8qCtdLWo [Congrats btw :)]
Well the ahadith about adhan and iqamah for the new born have many weaknesses, so especially for the iqamah some scholars tend to say the weakness is grave, and one shoould even consider this to be makruh or not mustahab (something not desirable) as quoted in this Arabic Fatwa.
Some if not most scholars say that the first thing the new born should hear are these words about the almightiness of Allah (see more interpretation of this here), while other scholars say one should do it when the kid got his/her name, so it could be done at the day of 'Aqiqa (~7 days after birth).
As the ears of a baby are much more sensitive then ours i would recommend to lower your voice way saying/reciting the adhan in the right ear, the iqamah (supposing this is regarded as a good deed) should be recited in the left ear.
And as an addition one could also follow the sunnah by feeding the new born with softened dates. This could be done by one of the parents.
Mostly it's the father who recites the adhan in the ear of the new born, but in some customs/traditions it's the grandfather (maternal), as we can read from the referenced ahadith our Messenger () did so for al-Hassan ibn 'Ali ()