First TEFL Lesson Interview is a good activity for a 1-to-1 lesson to break the ice and get to know your student. It can also be adapted for larger classes.
Quite simply, either before the lesson if you have the chance, or during the first few minutes of the lesson, ask your student to write down 10 questions which they would like to ask you. Tell them the subject matter can be about anything they like: personal life, love life, professional life… whatever they wish.
Then, take those questions and simply ask the student to answer them (you might have to adjust them slightly depending on circumstances); you can follow this up with further conversation and also answering the questions briefly yourself.
The idea here is simple. In a 1-to-1 lesson especially it is good for the student to talk as much as possible so rather than have you answer the questions, get your student to answer them.
Another useful aspect of this activity is that when the student is thinking about the questions they would like to ask you, they will use subjects which interest them so you will quickly be able to get an idea of what your student is interested in. For example, if they ask you which is your favorite football team then this is probably a subject which they enjoy talking about.
With larger classes you will need to break the students into pairs making sure they do not know their partner. Tell them to write 10 questions which they’d like ask and then once they’ve done this, simply get them to swap lists and ask each other the questions they’ve put down.