The first step in analyzing the poem is to look at its meter. Poetic forms are divided into stichic and stanzaic. Stichic forms are essentially continuous, rather than marked on the page or marked by rhyme as forming repeated multi-line units termed stanzas. The actual meter of My Last Duchess is heroic couplets, i.e. pairs of iambic pentameter lines that rhyme with each other. Characteristically of Browning, the lines often run over syntactically into subsequent lines, minimizing the natural pause on rhyme words, in order to achieve a more natural and conversational tone.
That's my last duchess painted on the wall,
Looking as if she were alive. I call
The first couplet introduces the painting of the duchess as though she were a display object in a museum, rather than a recently deceased wife. This sets up the relationship of the narrative voice of the Duke to the Duchess.
The first person point of view and speech addressed to an anonymous audience indicate that the poem is a dramatic monologue.
That piece a wonder, now: Frà Pandolf's hands
Worked busily a day, and there she stands.
The second couplet introduces the act of creation of the painting. Again, we get a sense that something`s not right in the state of Ferrara, because the Duke seems more interested in the showing off the fame of the artist than in regrets for the death of his wife.