How would you structure an essay around the premise that Frankenstein is "a novel about outsiders"?

Well, the first thing your essay should do is explain what you mean by "outsider." One thing you could discuss is the idea of an "outsider" as someone who is excluded from mainstream society, for whatever reason. Dr. Frankenstein, and his "child," the monster, could be compared using this theme.

The monster is most definitely an outsider -- not only is he shunned by his "parent," the Doctor, but his "monstrosity" makes him unfit for any sort of human company. We can see this at work in the part of the book where the monster hides and observes for many days the lives of the De Lacey family. The monster is moved by the loving example of the family, but when he makes himself known to them, they are horrified.

Dr. Frankenstein himself is an outsider as well -- but in a different way. His single-minded quest to understand the limits of mortality and master the secret of creating life alienates him from everyone else and leads to the death of his friend, Clerval, and his new wife. 

In both cases, the relationship of individual to society (their "outsiderness") is a function, in part, of the parent-child bond Frankenstein shares with the monster. The idea is that in forsaking his child, Frankenstein has ignored a basic rule of social responsibility -- raising your children. In a sense, it is because he repudiated the monster that they are both consigned to being outsiders.