Constantin Stanislavsky was an actor - considered to be a master in the art - and a proponent of the technique known as method acting. In the late 2360s, Data studied Stanislavsky's work in order to improve his acting skills, and found himself "particularly attracted" to the techniques described - noting Stanislavsky as one of his mentors. (TNG: "Devil's Due")
Stanislavsky was not actually a proponent of method acting. His "System" was used as a basis for that technique, and the two are often confused, although in reality they differ quite strongly - see The "System" versus "The Method" at Wikipedia.
Stanislavsky's name is more often transliterated with an 'i' rather than a 'y'. The script uses the 'y' spelling.