Hi, yes this may be a little hard to do without explanation. Let's see. A psychological approach takes into account why characters do what they do in a narrative. For instance, someone may lie because he/she is afraid of punishment. The whole school of criticism rose to prominence with the writings of Sigmund Freud at the turn of the nineteenth century, but was later amended by predominantly French thinkers such as Jaques Lacan and a number of feminists. When writing a character analysis that takes a psychological approach you can begin with looking at feelings, childhood experiences, motivations, connections to other characters among a number of things. It may also be helpful to consider when the text was written. If it is a modern text written within roughly the last fifty years or so, chances are the author may have deliberately or unconsciously incorporated Freudian insights.
Formalism is a little more tricky. Originating in the 1920's and driven by a desire to make the study of literature more scientific, Formalists are interested in the structure of language in a given text. Even though you did not mention what grade or year of school you are in, I assume that your teacher is simply asking you to take a closer look at the language in the text and analyze it for rhetorical figures for instance and consider how certain elements play into the overall effect of the narrative. It seems unlikely that you have to do a truly formalist analysis since it is more a theoretical approach one studies in graduate school.
You can, of course, combine the two and look for how certain states of mind are translated into language. Good Luck.