Hayasaka began his career with traditional music, and actually won some prizes before the war for his orchestral compositions. That gave him some real teeth when he moved to Tokyo in 1939 to become a movie composer. After the war, he got an invite from another composer, Akira Ifukube, to come work for Toho Studios. (Ifukube composed the scores for a number of Godzilla movies, as well as the popular Zatoichi films, which followed the adventures of a blind samurai.)
It was there that he met Akira Kurosawa, who gave him license to lay down the musical backbeat for his growing pile of notable films. They include a number of the director's early crime movies such as Stray Dog and Drunken Angel, his masterpiece Rashomon, and the drama Ikuru before Seven Samurai. He might have kept going forever, playing John Williams to Kurosawa's Steven Spielberg, had he not died of tuberculosis shortly after Seven Samurai was released. He was actually working on the score for another Kurosawa film when he died.
Hayasaka followed the tradition of Western composers, who developed individual themes for particular characters and events. He gives it a Japanese flair (the use of Japanese drums, for example), but you can spot the samurai's main theme pretty easily, for instance, and the themes recur throughout the film to give us a very specific emotional tag. Interestingly enough, you won't hear any stringed instruments in it. This is all for the brass, woodwinds and percussion, though he does let a guitar sneak in a couple of times.
He did that in part to make the film more accessible to Western audiences: to provide some sound cues to help ease us into a culture we didn't quite understand (and, let's face it, were fighting to the death just a few years earlier). We can follow a Japanese drama, but we don't have to listen to Japanese music in the process, helping the white folks of The Fifties not freak out so much at some of the ideas he wanted to explore.