This is a good question. First, let me give you some background information. It is difficult to know much about the historical Socrates, because he did not write anything. What we know of him is mainly through Plato.
What we do know is that he was executed for corrupting the youth in 399 B.C. From this point alone, we know that he had a special connection with the youth of Athens.
In light of this, we can make two point about how we can become more relevant teachers to the youth.
First, Socrates teaches us to question everything. This is a good starting point, because children love to question everything, especially authority. So, it might be a good idea to create an atmosphere of asking question. Learning takes place when questions drive students.
Second, Socrates really got to know people. So, he was more than a "teacher;" he was also a friend. This can give us a clue to good teaching as well. We should develop a rapport with our students that goes beyond the classroom.