I want to do a postcolonial literary criticism of the short story "How to date a brown girl (black girl, white girl, or halfie)" by Junot Diaz. How can I best write this essay?

First, you will need to decide what your thesis statement will be. Your thesis will guide the direction of your essay. So, in terms of postcolonial criticism, you might choose to discuss "othering," the idea of the colonized as an inferior character. By extension, you might also choose to focus on eurocentrism, the idea that everyone's experiences should be measured by European ideals.
Within a discussion of eurocentrism, you can discuss mimicry and double consciousness. Mimicry is the idea that the colonized can transcend his/her inferiority by mimicking the behavior, dress, and diction of the colonizer. Meanwhile, double consciousness refers to the idea that the colonized is in conflict. This conflict is the result of colonizing and colonized cultures warring for ascendancy in his/her consciousness.
So, your thesis statement could highlight how Eurocentrism motivates the narrator's behavior in Junot Diaz's story. Here are three examples you can discuss in your essay:
1) The narrator constantly portrays white girls as "premium" or prized females, the ones Hispanic boys (like himself) want to sleep with. With white girls, he is careful to "behave" as a white boy does. He resorts to mimicry, running his hand through his hair, and exhibiting an air of bravado. He even admits that he measures physical beauty through an European lens:

Tell her that you love her hair, that you love her skin, her lips, because, in truth, you love them more than you love your own.

2) Because of his eurocentric focus, the narrator often finds himself torn between his culture and that of the colonizer. He displays characteristics of hybridity but must constantly improvise, depending on whether his date is a white, black, Hispanic, or "halfie." According to the narrator, "halfie" girls understand him best, but they are also most particular when it comes to sexual intimacy. He stresses that white girls are more sexually adventurous. To placate the white girl, he must hide the "government cheese" before she comes over. In other words, he must keep his "welfare" background hidden from her.
3) The narrator also admits that he shares similar perspectives with the colonizer culture. He tries very hard to act and talk like a white boy. Yet, in certain settings, he feels that he must act "Hispanic," especially when it comes to ordering in a restaurant. The narrator isn't fluent in Spanish and actually prefers speaking English, much like everyone else he knows. However, he advises boys like himself to order everything on the menu in "busted-up Spanish."
You can probably come up with more examples of othering, hybridity, and Eurocentrism in the short story. Happy writing!
https://www.erhsnyc.org/ourpages/auto/2016/5/17/53610856/Postcolonial%20Criticism.pdf