The Mishna Brura in Hilchos Tisha B’Av brings a powerful hint as to what we should be doing on a fast day. It brings the Posuk within the story of Yonah – when he went to Ninveh to tell them to do Teshuva.
The posuk explains that the people of Ninveh fasted and donned garments made of sackcloth…and we are told that “HaShem saw their actions”.
The Mishna Brura explains “their actions” to be “teshuva” – ie. fasting and sackcloth did not sway the balance and despite fasting and being uncomfortable – it was their Teshuva that caused HaShem to spare their lives.
So too, when we are obligated by the Rabbis to fast, this is a smaller factor of the day.
We are only fasting to inspire us to do Teshuva and bring HaShem to our hearts.