If Beatrice were writing an obituary to fake Hero's death, she could use the standard technique and format. To write an obituary, you want the first line to state the deceased's name, age, residence and the date that he/she died.
We do not know Hero's last name, so we can simply use her first name. We do not know Hero's age, but we know she is of marrying age, which can be anywhere from 13 to 18. The play is set in Messina, so we know that that is where she would have died. We also don't know the exact time period that the play is set in, but we do know that the wars Don Pedro and Claudio have just returned from are the Italian Wars, which began in the late 1400s. However, if we were to set the play closer to Shakespeare's own historical time period, there were some Italian Wars in the late 1500s ("Timeline of the Italian Wars," Balagan). We know that the war Don Pedro and his troops just returned from was victorious because no important lives were lost, as we see from the messenger's line, "But few of any sort, and none of name," which was in reply to Leonato's question, "How many gentleman have you lost in this action?" (I.i.5-6). Since we know it was victorious, we can assume that the war was the one in which the Italians conquered the French at St. Qeuntin in August 1557. In the war that happened after that, Italy actually lost Messina to the Spanish. Hence, we can say that Hero was to be married and died around mid or late August of 1557.
If we were to write the first line of Hero's obituary for Beatrice, it might look something like this: "Hero, age 16, of Messina, Italy, returned to God on August 18, 1557."
The next line of an obituary tells a little bit about the deceased's background, such as where she was born and who her parents were. We know that Hero's father was Leonato and that she was born in Messina, so we can include that information as well.
We can also say whom she survived, which is her father, her uncle Antonio, and her cousin Beatrice. It is possible to state how the deceased died but it is inadvisable if they died under tragic or horrible circumstances as Hero would have done had she really died.
Finally, we give the details for the funeral arrangements. We know that she was to be buried in her families' tomb, so we can say something like: Funeral arrangements will be held at her families' tomb on August 19, 1557, at 11 am.