v1-2: The problem of Sarai's barren-ness; the suggested solution here which, although apparently successful, in that there is a son, brings strife into the household.
Sarai presented the solution, it was not borne out of prayer, there is no divine revelation. The course of action is of course acceptable in the culture of the day, and therefore appears to be reasonable.
It seems reasonable to suppose that Abram and Sarai acquired Hagar during their sojourn in Egypt. It was common practice for a family head to acquire slaves, sleep with them to father children by them. Abram seemed to follow the way of the culture, rather than trust in the promises of God.
v3: Abram and Sarai have now been in Canaan for 10 years; perhaps there is a growing impatience. Faith accepts God's timing as well as His will.
v4: Abram heeds his wife's voice, and goes astray. Hagar immediately conceives; success! Sometimes the way of human wisdom does have the desired results. But beware of later consequences! Here Hagar begins to despise Sarai.
v5: Sarai, understandably, blames Abram for the situation, for he is head of the household.
v6: Abram acts irresponsibly in allowing Sarai to mistreat Hagar. Throughout this incident, Abram submits to Sara's will, instead of taking the lead himself. Sarai mistreated Hagar; she went into the desert, meaning certain death unless God intervened.
v7: The Lord finds Hagar, and treats her kindly.
v8-9: The Lord deals also with Hagar; her attitude needs to be different; she was wrong to despise Sarai before.
The path of submission; thus the Lord will deal with us, rather than telling us what we may criticise in others. Faith involves kindness to others, whatever we think they deserve.
v10: The promise to Hagar, for her son Ishmael is a son of Abram, therefore he too has to be blessed. Later (chapter 21) Hagar and Ishmael are sent away again, and the Lord maintains His protection over them.
v11-12: Specific details of Ishmael's descendants; they will be aggressive, and live near to the family of Israel, which will bring further strife.
v13-16: The well, for Hagar the place of meeting with God.