How did Socrates practise critical thinking, and what is "maieutics"?

Through questioning — his "midwifery of ideas" (maieutiké techné): he didn't deposit answers but asked questions that helped others give birth to insight themselves.

Socrates likened his method to his mother's trade as a midwife: he claimed to teach nothing directly, but to deliver knowledge that was already latent in the other person, by relentless questioning. The Greek maieutiké techné literally means "midwifery art." Through a chain of probing questions, an interlocutor's confident but unexamined opinions are exposed as contradictory, clearing the ground for better-founded belief.

The takeaway for critical thinking: the engine is the question. Asking "why do you believe that?" and "does that follow?" — of others and of yourself — is the oldest tool of the discipline.