How is the ending of Romeo and Juliet the result of human actions rather than fate?
A good question.
Actually, for all that the chorus calls Romeo and Juliet a "pair of star-cross'd lovers" in the prologue, just about all of the action in this play is due to human choice and action, including the ending.
True, neither Romeo nor Juliet chose which families to be born into. That aspect of the play (and their situation) could be considered fate. However, once they start acting, they are choosing their consequences, including the ending of the play. Take, for example, Romeo's actions in Act I, Scene 1. When Balthasar tells him Juliet is dead, he decides to kill himself. That's not fate. It might be passion, but it isn't fate. It also means he chooses not to do other things. Romeo does not check to see if Juliet is dead, doesn't decide to live in her memory, etc.
Likewise, when he finds the apothecary to sell him the poison, the man chooses to break the law and sell him that poison. That's not fate. That's choice. When Romeo and Paris fight (later in Act V), it isn't fated that they fight. They might have talked things out. When they do fight, it isn't fate that Romeo's the one to win, and so on.
At each point, the characters choose their ends. This includes Juliet stabbing herself.
There is an argument to be made that it is actually fate that directs the events which occur. The Chorus, of course, initially tells us that this "pair of star-crossed lovers [will] take their life" (Prologue, lines 5–6). In other words, the destinies of Romeo and Juliet were decided even before their births; they could not have done anything but fulfill them.
Later, Romeo's friends try to convince him to go to the Capulets' party with them. He really doesn't want to go and argues vehemently against it. Finally, however, he relents, saying,
. . . My mind misgives
Some consequence yet hanging in the stars
Shall bitterly begin his fearful date
With this night's revels, and expire the term
Of a despised life closed in my breast
By some vile forfeit of untimely death.
But he that hath the steerage of my course
Direct my sail. (1.4.113-120)
Now, Romeo admits that he feels fate is directing his actions. Again, someone refers to the "stars" and the influence they have over their lives. Romeo believes that going to the party will set into motion a chain of events over which he has no control, and yet he also feels compelled to go by whoever or whatever "hath the steerage of [his] course." He knows, however, that it will end in his death.
Later, despite Benvolio's warnings, Romeo, seemingly without thinking, kills Tybalt after Tybalt slays Mercutio. Once he realizes what he has done, Romeo cries, "O, I am Fortune's fool!" (3.1.142). Again, he blames fate for the events which have transpired. Then, when Balthasar tells him that Juliet is dead, and the Friar's letter has not been delivered, Romeo shouts, "I deny you, stars!" (5.1.25). He certainly feels like a victim of fate, and despite all the attempts both he and Juliet make, it does seem as though, no matter what they do, no matter how much they plan or try to make things turn out differently, they can only end up as victims of fate.