The word "approach" is in the title, but mostly what happens in the song is the "yearning" part.
In this love song, it is unclear whether the speaker has broken up with the woman in his "dream," or if they have never had a romantic relationship to begin with. He does know her-- he can "distinctly hear" her voice, and is perhaps a friend. (In the version on In the Blue Light, the line becomes "I can hear your secret voice," implying intimacy, not simple acquaintanceship.)
But whether they were a couple before or not, they are not, now. And this is making him both "blue" with disappointment and "feverish" with desire.
The song is rich with the imagery of places. It begins in a motel room. The speaker is probably lying on his bed with the TV on, but he is not watching it. He is lost in thought, "wondering" how to "approach" what he "yearns" for. Then the song moves to "the side of the road," "the top of a hill," and a "phone booth at a local bar-and-grill" (in the In the Blue Light version, it becomes a "downtown bar-and-grill.")
There are even abstract places, like a "fever" and a "dream."
The song is also replete with the image of heat. First, the television passively "burns." Then, he has a "fever"-ish dream, from which he cannot wake. In the dream, there is "heat" and "fire."
After the speaker tells us about ignoring the TV and having his intense dream, the song shifts focus to another character, "a bone-weary traveler." Is this an actual person, or a dream image? Is the traveler the speaker himself? We know that he is in a hotel, so he is himself traveling. But he is not "by the side of the road," he is safe in a hotel bed. Unless he feels like he is "waiting by the side of the road."
About this man, the speaker wonders, "Where's he going?" If it's the speaker, we presume that he is in a motel as a stop-over on the way to a known destination. So if the question is metaphorical, the "where" could refer to where he is going in life-- toward his dream-woman or away from her.
Incidentally, it is "after the rain." This water image counters the hot images found elsewhere.
Now, we get to the dream. He does not dream that he and his would-be lover are marginalized "by the side of the road. Quite the opposite-- they are "lying on top of a hill," and are evidently making love. Again, the imagery is of heat: "Your voice is the heat of the night/ I'm on fire." (The In the Blue Light version eliminates the "I'm on fire" line. While this line predates the Springsteen song with this title by four years, that song is much more famous and Simon might have felt he would sound like he was quoting Springsteen instead of vice versa. Or maybe he just thought it was cliche.)
Notably, the entire line "I dream we are lying on the top of a hill" is not sung in the In the Blue Light version. The lack of this line, however, means it much less clear that the "rolling" business is only a dream. It could be an extension of the line "emerging from a dream, the dream returns" but there is a whole bridge about a "traveler" in between now. That, coupled with the knowledge of the "secret" voice, seems to imply the woman in question was a close friend or even a former lover, not just a passing acquaintance.
Enough "yearning"-- time to "approach." He calls her on a pay telephone at a bar. He does not get through, and his coin returns. He "approached," but so far he has not "reached."
He is in a state of coolness and passivity except when thinking about this woman. Aside from the cold/hot images, we have various verbs relating to passivity, lack of movement. When fantasizing of her, he "wonders," he "hears" (he never speaks to anyone in the course of the song), the traveler "waits," and he "rehearses," (but again does not get the chance to speak or perform).
But when he imagines himself with her, he becomes more active, and sees himself "rolling" in her arms. Ultimately, even in the case, he does not see himself as active-- he is in her arms-- she is holding and encompassing him, in his conception of the embrace, when presumably they would be holding each other. Alternately, the line could be "I roll you in my arms," in which case he would be the active one.
Two verbs more are repeated. One is the word "returns." First, the dream-- the one so intense he cannot wake from it-- returns (in the In the Blue Light version, her "voice" returns). Then when he tries to call his dream lover, his coin returns as well. He is moving in circles, returning and returning and never progressing-- yearning and approaching but never attaining.
Then the line "headlights slide past the Moon" is repeated in its entirety. Both the headlights and the Moon are round and yellowish and glow in the night. As enormous as the Moon is, is can appear as small as a headlight in perspective.
So we have the contrast of one light staying still, and a set of two lights moving "past" it and leaving it behind. This might be a symbol for his situation and desire. If he is one light, like the Moon, he stays in place-- wondering and waiting "by the side of the road." But if he were paired with her as headlights are, the two would "slide"-- with no friction-- on the "interstate," right past such a lonely moon... or roadside traveler.
Even the roadway itself is different to him when he sees himself with her. When one is "waiting on the side," it's just "a road." But to those "sliding" along it together, it is a sleek, wide "interstate."
Ultimately, he is no further along at the end of this series of events than when he started. The question is, now that his coin has returned, does he return to the phone booth to try her number again? Has his courage been permanently raised?
Well, there is no more imagery of heat, or movement, in this verse. Even the bar is "some local" one. So has this simple disappointment brought him back down to the level of despair again? Yeah, that's more likely the case.
In the version
Next Song: Oh, Marion