It's worth noting that Juliet's "death" isn't really her death at all in this context. Instead, she has taken a strong sleeping potion that makes her appear dead in an effort to escape and live with Romeo. Friar Lawrence actually pens a letter to Romeo to explain this scheme to reunite the young lovers, but in perhaps the most tragic turn of events in the play, the letter never makes it to him.
News quickly spreads of beautiful Juliet's "death," and Balthasar, Romeo's servant, goes to Mantua to tell Romeo of this tragic turn of events. Romeo is, of course, immediately and visibly upset. Balthasar notes:
I do beseech you, sir, have patience.
Your looks are pale and wild, and do import
Some misadventure. (V.i.27-29)
Romeo asks if Balthsar has a letter for him, but he finds a dead end there. He therefore makes the immediate decision to find an apothecary and purchase a poison to end his own life. This sets in motion a series of events that will lead Juliet to her real and actual death.
In Act V, Scene 5, Balthasar watches the body of Juliet put to rest in the mausoleum of the Capulets. He then speeds to Mantua to tell Romeo of this tragic incident. Meanwhile, Friar Laurence had sent a letter to Romeo telling him about the plan for Juliet to awake, but the Friar that was bringing the letter to Romeo was delayed and Balthasar beat the Friar there.
Without knowledge of the arrangement between Juliet and Friar Laurence, Balthasar sees Juliet being buried in Capulet’s tomb. Balthasar automatically assumes Juliet is really dead. In act V, scene i, Balthasar rides to Mantua to tell Romeo of Juliet’s recent passing. The letter explaining the strange circumstances was detained due to the quarantine so Romeo was never able to learn about the lengths Juliet has gone through to be with him.
Romeo learns of Juliet's supposed death from Balthasar in Act V, Scene 1. Friar Laurence had sent Friar John with a message for Romeo to let him know that Juliet was in fact still alive, but it did not reach Romeo in Mantua in time because Friar John was quarantined.