Answered by Sayyidi Habib Umar bin Hafiz (may Allah protect him and benefit us by him).
What should our intentions be upon entering Ramadan?
We should intend to be in the state that Allah and His Messenger ﷺ love for us to be in.
We should seek to attain Allah’s pleasure and to perfect our following of the Messenger of Allah ﷺ so that we attain his companionship.
We should intend that a new door is opened to us in understanding the Qur’an and acting according to it.
We should intend to avoid the inward things that nullify our fast just as we avoid the outward things.
We should truly seek to raise our fast from the fast of the ordinary people to the fast of the pious and we should aspire to attain the fast of the elite even if only for a short time.