How do you write a literary criticism of The Mill on the Floss? I don't know what to write about. We want to keep the essay confined to the story...

There are several different approaches you could take to the assignment. The key to writing a critical paper of this type is to focus on one very narrow topic you can investigate in depth.

A key to writing a good paper—and actually enjoying the experience—is to find some connection between your own interests and the novel. For example, if you are majoring in business or accounting, you might look at the economic role of the mill or the finances of the Tulliver family. You could analyze, from a business perspective, whether Mr. Tulliver was a competent manager. 

If you are majoring in engineering, you could write about whether Eliot's portrait of the mill was accurate and perhaps investigate how mills were built in the period, how they worked, or their importance to the economies and industries of small villages.

If you are interested in fashion, you could talk about the descriptions of the clothing of two or three characters in the story and what those descriptions tell us about them.

Another possibility would be to discuss Philip and the views of disability in the novel. You could contrast how different people respond to Philip or discuss the mechanisms Philip uses to cope with everyday life. 

If you enjoy boating or outdoor adventure, you might want to analyze the episode of Stephen and Maggie in the boat, looking at whether it is credible or contrived. 

Another possibility would be to discuss the ending and whether it is justified or contrived. One can argue that the ending is a way of emphasizing that Maggie has no place in England as it exists, and that there was no real space for an intelligent woman in her society (a feminist argument), or you could argue that the ending is too artificial and too easy, simply killing characters off rather than actually resolving the conflicts of the story. 

For a scholarly article, once you have narrowed your topic, you should visit your university library website and look for the MLA International Bibliography. This database includes links to hundreds of scholarly articles on this novel. You can look at the titles of the articles and their abstracts to find one relevant to your topic.