"The which, if you with patient ears attend...." is part of the prologue for Act I. No specific person is specified to speak this part (which probably triggered the question), so there is a variety of choices here. The play's director would determine who would deliver the prologues and how.
From what I read, historically the prologues are delivered by a chorus (I envision a similarity to Greek theatre here). The director can also appoint a narrator, of course, which probably would work better than a chorus, as the well-spoken words of one person are easier to understand (particularly in the cheap seats) than those of a group of people speaking as one. In movie productions, other choices are sometimes made. In the 1996 film version (Romeo + Juliet), a news reporter delivers the lines as an evening news story.
One of the many beauties of Shakespearean plays is their versatility throughout time, limited only by the imagination of the plays' directors.