Getting "In"

How do you get into a narrative or story to the extent of causing the reader to feel the connection?

You begin by remembering the importance of every scene in the narrative; each must make a contribution of feeling relevant to one or more of the characters or to the theme.  Even better if you can hit a twofer.  Then you remember the need for the entire piece whether short form, novel, essay, or memoir, to arrive at an aggregate emotional payoff.  It is not an ending until it has an emotional impact.  It is not emotional if the reader either feels nothing or finds him/herself being argued into feeling something.

Suppose my story is epistolary, such as Gilead by Marilynn Robinson? Or maybe even Ring Lardner's You Know Me, Al?

Nevertheless.

Look at the effects Cynthia Ozick achieves with the letters written between brother and sister in Foreign Bodies.  Every one of them not only conveys emotion, they show background, attitude and character development.

Let us see characters believing in the hopelessness of their desires yet still holding onto them.

Let us see characters doing something against a background of some debilitating emotional or moral tugging at their coat sleeves, or, perhaps try the man-who or woman who approach, as in the man who wore out twenty pair of hiking shoes in his trek across America, or the woman who'd been married three times before she reached age twenty.

If it is to be done using dialogue, do not be literal, as in "I see in you a man of great purpose and unwavering determination."  Even though other characters can be more reliable sources of information about your front-rank players than you can, dialogue works best when the lines are delivered against an ironic counterpoint, Sisyphus, for instance, saying, "Gotta run now,  My rock is due for its fifty-thousand-mile check up."