I don't achieve complete student engagement with every class, but I'm happy about the times I've succeeded, and I've learned a few things about motivating my students: they are competitive and they like classroom games where small teams compete against one another. They like role-plays. They like debate, although not every student has the command of English to meaningfully participate. Some students would not speak at all. One little innovation I started was to make every roll call into a poll on some question we were discussing in class. For example, today we acted out a short radio play about a mad scientist looking for the abominable snowman. The play was unfinished. So I asked the students as I was taking attendance, who won, the snowman or the scientist? Or, a tip I learned from my ESL teacher; stand at the doorway at the end of class. The students can't leave until they each answer a question (such as, "what are you going to bring to the picnic?" "My name is Paula and I'm bringing peaches, my name is Linda and I'm bringing lemonade," and so on.
The absolute best times are when I've succeeded in creating chaos in the classroom, when (almost) everybody is on their feet and talking. One time that happened was when I created a role play activity around buying and selling.
I wanted to show a video clip of the students fully engaged in their role play but I also wanted to respect their privacy. Thanks to special effects, I can show the clip with the students "ghosted" out. The students are holding "buyer" and "seller" cards, transacting deals over cars, washing machines and television sets.
By the way, 95% of my students are girls. So heck yeah, I'm playing to my audience; topics include the Titanic movie, fashion, wedding dresses, the Backstreet Boys, and so forth.