On several occasions of my first-round faculty interview, I was asked about the diversity questions, such as: "How do you work with diverse students?" "How do you contribute to the university's diversity mission?"

Well, how do you work with diverse students? Do you contribute to the university's diversity mission?

If you can't answer those questions right now, then perhaps the sad answer is that, right now, you're not contributing to a mission the university has decided to care about.

I want to seek some insights into the questions. Which aspects I need to cover to delivering a winning answer?

Like paul garrett says, it's not about about memorizing a "right" or "winning" answer, but about demonstrating that you care about these issues and have been thinking about them.

I don't mean to slam you here. Asking what aspects you need to look at is a good question. I'll try to help.

So, how do you work with diverse students?

Things to think about: what kind diverse students have you come across? Which ones haven't you come across - or haven't noticed? If for example you say "I've never had a trans person in my class", are you sure? Maybe they weren't out. Awareness of diverse students is an aspect here.

Do you have biases? (Be honest with yourself. Ask friends who aren't afraid to tell you things you're not happy to hear.)

What kind of issues do diverse students face in your field? Are there poorly represented groups (like women in STEM fields)? Note that some issues are due to prejudice, but others are more justified/neutral. For example, foreign students can be at a disadvantage because they don't have native mastery of your local language, or have trouble adjusting to the local academic culture. That doesn't mean anyone is evil, but it is an issue to pay attention to.

How could you contribute to the university's diversity mission?

If you've identified issues, then it becomes easier to come up with contributions.

You might serve as a role model yourself, if you fit into a traditionally disadvantaged group.

You might pay extra attention to (subtle) discrimination in the classroom and deal with it.

You may have done research about didactic technique to help foreign students adjust better.

Etcetera. The point is not to have a glib answer, but to actually be working on these issues. That takes a significant amount of work and soul-searching. Discuss with your peers. But also go out there and seek conversational sparring partners in "diverse" groups and ask them about their issues. It can be easy in the ivory tower to not see any problems, you may have to go outside looking for them.