One of the characters that explains the entire story of what happened after Romeo and Juliet met is Friar Lawrence. After the deaths of Romeo and Juliet, Prince Escalus and the two families come together. At this point, the Friar explains everything that took place. The Friar's speech begins,
Lawrence proceeds to tell of everything that took place, from the wedding of the two to the plan for Juliet to take the potion, up until their tragic deaths.
The two characters you're looking for are Benvolio and Friar Laurence. At separate - parallel - points in the two halves of the play, Benvolio and Friar Laurence both narrate the events that have happened. It's interesting as to whether we actually believe them - particularly in Benvolio's case, there can sometimes be an obvious tension between the events as we've just watched them, and the description we are now hearing.
Benvolio's speech starts like this:
O noble Prince, I can discover all
The unlucky manage of this fatal brawl.
There lies the man, slain by young Romeo,
That slew thy kinsman, brave Mercutio.
He then goes on to describe in detail the fight and how the two deaths have occurred.
Friar Laurence's, in Act 5, Scene 3, begins like this:
I am the greatest, able to do least,
Yet most suspected, as the time and place
Doth make against me, of this direful murder;
And here I stand, both to impeach and purge
Myself condemned and myself excus'd.
In Shakespeare's source for the play, the Friar was hanged. At the end of R&J, judgement is still suspended on Friar Laurence - and whether you think that is right or not depends largely, I think, on how that speech is paid.
Hope it helps!