One device utilized in this poem by Browning is that of setting. The location of the poem is very obvious "famous Hanover city". This Germanic setting of the poem is very effective because it the audience is reminded of children stories by the likes of the brother's Grimm- who's cautionary tales were often set in central European settings.
Browning's use of rhyme is is another effective way in which the story is told, in most cases each two lines rhyme or the scheme is a A B A B pattern. This is effective is several ways: one being that it reflects the rhyme scheme of children's cautionary tales such as nursery rhymes; and also makes poem very song like- which reflects the fact that the protagonist (the pied piper) is a musician.
Similarly there is a use of musical imagery throughout the poem- i.e. the noises made by the rats are described as "fifty sharps and flats" meaning the audience is inconstantly reminded of the protagonist's craft as a musician.
Their is a clear juxtaposition between the towns people (specifically the "corporation), and the eponymous piper. While we are very aware of the towns people's origins (Hanover city), the language used to describe the pied piper mark him out as different. His dress is describe as "quaint" and at one point he is referred to as a gypsy having traveled to exotic lands such as "Asian the nizam". He also described as thin, whereas the mayor of the town is described as fat. This juxtaposition is effective because it foreshadows the conflict between the two characters later in the poem.
The linear chronology of the story is used similarly to the other structural devices used in the poem, to mirror the simplicity in which children's stories are told- therefore effectively reflecting the sub title: "a child's story".
There is an effective use of enjambment in stanza two with the word "Rats!", this is particularly effectively because it is separate from the rest of the poem so it jumps off the page, much in the way a rat may jump at a citizen of Hamlin.