The beat is the first thing you hear. It's about as simple as a beat gets, too, with hits on the hi-hat every eighth note and alternations between the snare and the bass drum every quarter note. Drum fills are minimal. Things stay more or less the same throughout the entire five-minute piece, which is a good thing because the beat is infectious and somehow immediately recognizable. In mixing the song - giving the song that "sonic personality" (whatever that means!) - Swedian recalled that what he ended up doing "was building a drum platform and designing some special little things, like a bass drum cover and a flat piece of wood that goes between the snare and the hi-hat. The bottom line is that there aren't many pieces of music where you can hear the first three or four notes of the drums, and immediately tell what the piece of music is."
After a bar of the beat, that iconic, prowling bass line lurks into the mix. The bass line is what's called a "walking bass line." Typical of jazz or the blues, walking bass lines typically follow chord changes in a song, but they are most essentially characterized by their equal note value and a melodic quality that rises and lowers steadily (like the rhythm of walking). The main bass line to "Billie Jean" has all of these qualities. The verse chord progression begins on the F# minor chord, and the bass line bounces between tones in that scale, with equal eighth notes all the way. When the chord bumps up to a B minor at "Who would dance on the floor in the round," the bass line jumps up as well.
The only other core instrumentation is the keyboard, with that simple four-chord progression from F# minor to G# minor and then to A minor, and back down again. As Phillinganes pointed out, the minimalism allows everything to stand out. Each instrument can be individually appreciated, which is partially because the bass and the beat are more or less mixed evenly with Jackson's amazing lead vocals. Jackson has said that he writes his vocal melodies to demonstrate his vocal range, but Jackson is somewhat conservative when it comes to melody in this song, focusing more on rhythm, letting his now signature vocal hiccups define his lead vocal. His range is better demonstrated by his back-up vocals, which were sung into the microphone through a six-foot tube. His back up vocals make up most of the instrumentation in the song, and have an improvisational quality as a kind of emotional Jackson responding to the lead vocal and featuring his high-pitched "hee hee" vocal signature.
The funny thing about it all is that while everything in the song works so well, the song's producer, the famous Quincy Jones, didn't want to put Jackson's song on the album at all. He did not feel that "Billie Jean" was strong enough to cut it on Thriller, Jackson, though, was convinced it would be a hit and had a lot of input into the final sound of the track, even asking Jones for a co-producer credit. Though Jones didn't give him that, Jackson clearly deserves most of the credit for getting the song out there. As he said in a later interview, he demanded the song be on the record because musicians simply know when they've got hit material on their hands.