So god finally makes good on his promise that Sarah will bear a son to Abraham, even though Abraham is 100 years old at this point. The little baby boy, Isaac, is duly circumcised. Understandably, Sarah is thrilled that after all this time she finally has the baby that she wanted.
What happens next is a little less understandable (well, perhaps understandable but certainly not justifiable). She sees Hagar's son, Ishmael, playing with Isaac, and Sarah decides she wants both Hagar and Ishmael kicked out so as not to imperial Isaac's inheritance. Considering the whole plan with Hagar was Sarah's idea in the first place, this seems especially cruel.
Abraham is reluctant—Ishmael is as much his son as Isaac is—but god tells him that it will be okay, because Isaac is the one that god will use to fulfill all his covenants about the multitude of offspring. God does relieve a bit of Abraham's worry by agreeing to also give Ishmael a nation of descendants, so Abraham gives Hagar some bread and water and boots her and Ishmael out.
Hagar wanders around in the wilderness around Beersheba until her water runs out. Which was pretty inevitable because it's a freaking desert. Reasoning the likely end of this, she sets Ishmael under a bush and walks away so she won't have to watch her son die. While she is crying over all this, god sends an angel to tell her that he heard the cries of her and her son, and that he will make a great nation from them. Then Hagar sees a well and her and Ishmael go on to be happy wilderness dwellers. Ishmael even gets an Egyptian wife. So I suppose that totally makes up for being dismissed from your home for following orders and having the father of your son abandon all responsibility for you.
Then we switch gears back to Abraham. Abimelech (yes, the one who was tricked by the Sarah-is-my-sister routine) realizes that Abraham obviously has god's favor, so he wants to make a pact that he and Abraham will treat each other loyally. Abraham thinks this is a good deal, probably because he is still an alien in the land, and so they agree. Later Abraham complains about some of Abimelech's servants seizing one of Abraham's wells, and Abimelech takes care of it when Abraham gives him some lambs (seven, an auspicious number). It's a pretty boring story, honestly, but it explains why Abraham was able to live in relative peace as an alien with the Philistines.
Well, jealous mothers, thirsty babies, and plain old politics, there we have it for Genesis 21!
15 minutes ago