In "Shooting an Elephant," how does Orwell convince the reader to trust him? What does Orwell do that convinces the reader that he is honest?

I'm not sure Orwell does, or that it matters. You can read this story as a brutal kind of entertainment, and not consider the issue of trust at all. So, that is one option.

If you really want to examine what Orwell does to gain the reader's trust, start with the opening line, where Orwell says he was hated by a lot of people. That might not gain your trust, but it should tug at...

I'm not sure Orwell does, or that it matters. You can read this story as a brutal kind of entertainment, and not consider the issue of trust at all. So, that is one option.

If you really want to examine what Orwell does to gain the reader's trust, start with the opening line, where Orwell says he was hated by a lot of people. That might not gain your trust, but it should tug at your sympathy, which contributes to trust. Orwell continues this practice throughout the first paragraph, isolating his narrator (himself), and documenting his suffering.

He then follows that in the second paragraph through the perspectives he admits. When he says "imperialism is an evil thing" and shares his plans to quit his job, he's sharing confidences with the reader. If someone shares something with you he has reason to keep quiet, you're more likely to trust him.

Another way Orwell gains reader trust is through the many specific details included. From the "betel juice" locals would spit on a European woman's dress to the fact that he knows a lot about elephants, Orwell sounds like an authority, almost a local guide. Readers have good reason to trust him.