The most important thing before writing any form of literary analysis is, without a doubt, to properly read the work or book to be analyzed. It could be either a short story or a children's book, a novel or even an essay. Depending on the type of literary work you are analyzing, you have to read according to a different set of guidelines; while the novel is the longest but easiest form to analyze, the essay is the hardest of all.
Once you know the time when the work was written and the audience it was directed to, you have to focus on the influence it might have on the people who receive it. You should try to identify the work's message or moral, as well as the literary language being used by the author, the most frequent expressions, metaphors, literary figures, etc.
The argument can be taken as a summary that clarifies the author's main ideas, and that tells you what the essence of the work is. You can list the main characters in the work and highlight the characteristics that define them, always from the point of view both from the author and from the reader, since they can have different ideas as to why a certain character might be good or bad.
In the end, the goal of a literary analysis is to capture all the characteristics of a literary work, viewed from every possible perspective, and not only from that which corresponds to a specific location or time. This way, anyone can achieve an understanding of the work, even if your culture is very different to the author's, or if you live far in the future from the author's time.
Finally, you can add to your critical analysis your own opinion. You can allow yourself to get carried away, and give any opinion you want. You can express your own ideas, having a clear stand for or against the work. You can say if you liked it or if you hated it, your opinion on the ending, and if you would or wouldn't change anything.