How did Poe, Twain, Hawthorne, and Melville believe one should act in order to live life to the fullest? Some of the assigned readings for this...

First, according to a search on the Google Ngram viewer, this particular phrase "living life to its fullest" originated in the 1920s, had a few brief years of moderate popularity, and then did not resurface until the 1960s. It gained traction with the popular self-help movements of the late twentieth century and has continued to be associated with popular self-help fads in the twenty-first century. Since all of the authors you mention lived in the...

First, according to a search on the Google Ngram viewer, this particular phrase "living life to its fullest" originated in the 1920s, had a few brief years of moderate popularity, and then did not resurface until the 1960s. It gained traction with the popular self-help movements of the late twentieth century and has continued to be associated with popular self-help fads in the twenty-first century. Since all of the authors you mention lived in the nineteenth century, it would be chronologically impossible for them to have expressed positions derived from twentieth-century self help movements.

Various different works by these authors show different obstacles to leading happy and fulfilling lives. In many case, the obstacles are external circumstances. An epidemic of bubonic plague, the Spanish Inquisition, and slavery are among the external obstacles to living some form of good life in various works by these authors. For Twain, authority figures and middle class conventions can serve as obstacles. 

Poe often creates narrators whose own twisted minds are their worst enemies. The narrator of "The Tell-Tale Heart" is haunted by his own paranoid delusions. In the case of Montresor in "A Cask of Amontillado" one could argue that his obsession with revenge warps and twists his life, but the tone of the story suggests that in fact pursuing and fulfilling his plot for revenge against Fortunato has given him a certain degree of satisfaction. 

Hawthorne and Melville both had strongly Calvinist family backgrounds and their works often have strong religious themes, and a particular awareness of original sin and the inherent darkness of human nature. To achieve some sort of fulfillment in their lives, characters struggle against the evils in their own nature, including in particular the vice of sloth or complacency, i.e. the temptation to take the easiest or most comfortable route in life.