How did Emily Dickinson's life affect her work? Discuss at least one poem in detail.

Firstly, I can recommend two excellent biographies of Dickinson to help you: The Life of Emily Dickinson by Richard B. Sewall, which is the seminal biography of Dickinson, and My Wars Are Laid Away in Books by Alfred Habegger, which is the most recent biography.  
Gardening and the study of botany were important interests of Dickinson's. She loved flowers, particularly those which produced a fragrance (she cared less for orchids due to their lack of aroma), and spent a lot of time caring for flowers in the greenhouse at her family home in Amherst, Massachusetts. Many of her poems are about flowers, though, in some verses, she may be using flowers as a metaphor to explore other ideas. Please consider the following poems as examples: "I hide myself within a flower," "The Lilac is an Ancient Shrub," and "Pink—small—and punctual—." The last of these is said to have sexual connotations, though it is also about a perennial flower. 
For more information on how gardening and botany affected Dickinson's work, as well as more information about the flowers for which she cared, consult The Gardens of Emily Dickinson by Judith Farr and Louise Carter.