The best way to analyze a song is to ask yourself critical questions about the piece of music you wish to analyze. Let’s take a look at some questions in some of the categories you mentioned, with an eye for how each category contributes to the overall feeling, message, and emotion of the song. As a previous answer to this question did an excellent job of breaking down some of the specifics here, let’s zoom out and ask some why questions.
Let’s start with rhythm, tempo, and beat--- the rhythmic components of the song. What effect is created by the variation in the rhythmic quality between the first and second rendition of the chorus? What about the rhythm makes (or doesn’t make) the song “catchy” and worth listening to?
Melody: There is not much variation in the melodic line of the verse compared to the chorus—what effect does this have? Why would Taylor choose this kind of melody? Does it “work?”
Timbre and texture both refer to the type and structure of the instrumentation of the song. How would the song be different if Taylor had chosen to use different instrument? What if she were singing alone with no accompaniment? An Orchestra with no drums?
Dynamics: How does Taylor use dynamics to add emotion to the song?
Your goal with all of these questions should be to think about why things are the way they are in the song, and if it “works” the way it stands. If not, perhaps you could think of ways that, if you were Ms. Swift, you would improve upon the song!
A great way to begin your analysis is by looking at the structure of the song as a whole:
A (Verse [I was reminiscing...])
B (Chorus [Darling it was good...])
A (Verse [Spinning like a girl...])
B (Chorus [Darling it was good..])
C (Bridge [Tonight I'm gonna dance...])
B (Chorus [It was good...])
C (Bridge [Tonight I'm gonna dance...])
Now that we've seen the breakdown of the song's structure, we can see how different musical elements appear in each section.
Notice that each verse (our A sections) has a 4/4 time signature and a moderately fast tempo. The drums thumps along like an excited heartbeat. In the verses, the lyrics emulate the pace with lines like "took off faster than green light, go" and references to "New York time."
The first chorus (section B) is a sudden transition to a more reserved, almost somber tempo. The beat takes a break, allowing the vocals to take the lead. Here, the dynamic transitions to more of a hushed mezzo-piano. As she sings the words "Holy Ground," the beat returns to the chugging tempo of the verse.
In the second verse, we hear a true contrast in dynamics. From the soft mezzo-piano of the chorus, the second verse builds up to mezzo-forte with the line "I guess we fell apart in the usual way..."
As opposed to the first chorus, there is no absence of the beat in the second chorus. Here, the strong thudding beat drives the vocals into the chorus. Whereas the first chorus felt like a prayer, the second chorus is more of an anthem. We are treated to complimentary harmonies and soaring vocals layered throughout.
These cooing vocals bring us into the bridge (section C). The first "Tonight I'm gonna dance..." is punctuated by a sustained guitar chord held for 8 counts throughout each vocal phrase of the bridge. For the second "Tonight I'm gonna dance...," the guitar returns to its usual strumming pattern, building the intensity through the line "like you were in this room." The last two words of the bridge ("with you") drop to a piano dynamic with a sweet, plaintive tone.
Again, we are brought into a mezzo-piano chorus with the steady back-beat. This chorus begins with minimal guitar (traces of syncopation after each of the first two vocal phrases), but builds to mezzo-forte through with strong vocals through the line "Right there where we stood."
With the final "Holy Ground" of the song, we are reintroduced to the vocal layering from the first chorus. The second occurrence of the bridge starts out with a fierce forte dynamic, bold and unapologetic. A final sustained guitar chords strips the song's ending to bare vocals for the mezzo-piano line "if I'm not dancing with you."