First, you have to actually be an excellent teacher. My suggested path to that is to focus on student learning, not lecturing, and to dedicate yourself to teaching every student who has a desire to learn. Big job. Hard job. It might take you (them?) some research to see how to do that and to practice it. It would also, to me, imply, a fairly robust and active classroom environment, provided that the scale permits it. Lots of questions to and from students, perhaps. To do it well, you need to be available to students even outside of class. Even online.
One way to gain the needed skill is to ask a colleague known to be an excellent teacher, even someone who previously won the award, if they would permit you to visit a few of their classes and then discuss techniques with them afterwards. Repeat as needed, perhaps with other colleagues.
Next, you have to be recognized as such. One way to do that is to get involved with organizations in your (their?) field that focuses on education. In CS that would be SIGCSE, for example. Contribute to their conferences and such.
Locally, once you (they?) have “mastered” the task, invite a faculty member or two, and the chair if necessary, to visit your classroom and give you feedback on your presentations and interactions. Can you bring out the “quiet” students, who sit in the back? Can you make it interesting without it being chaotic? How do you respond to questions, especially seemingly hostile or disruptive questions?
But to me, the biggest part is dedication to teaching every student. Not just the best, not the average; all.
No, I never won teacher of the year, even after I learned and practiced the above. I won some other rewards, but that one evaded me. And, confession, at the beginning of my teaching career I was overly pedantic, thinking that the perfect explanation would resonate with every student. It took me years to learn that students in my classroom weren’t like me: driven to study this field without compromise. They have other goals.
A note on scale. It is unlikely at the sort of institution you describe, but if a “class” has 200 students, then an “active classroom might be impossible to manage. In such a case there are hopefully enough TAs (8 or so) to manage breakout sections for students to get questions answered. One technique in such a case is to make the rounds of those sessions, visiting each one occasionally as an observer and source of information as well. A visible presence is helpful.