The easiest thing to do is just map the song out yourself measure by measure. First figure out what the time signature is (4/4 usually), then map out the number of measures in each phrase or section (often 8 bars each to the verses and chorus, for example). Then after you map those out, look at the chord sequences. How does the harmony change from measure to measure or from phrase to phrase? Then look at what the melodies are doing, and finally any other little details that add to the overall experience of the piece.
In some of the best classical music, the composer takes some small motif, maybe even just a few notes, and then expands those to create the structure of the entire rest of the piece. Beethoven was a master of this. The first notes of Beethoven's opus 131 string quartet basically lay out the key signatures of each movement that follows. Those same notes also create the feel and set the tone for the entire rest of the quartet, which is about 40 minutes long. Fortunately most songs today aren't nearly that complicated. They mostly reuse the same structure, phrasing, and chord progressions, so once you become familiar with them you can start getting creative with them yourself.