Here's how it's done in Dostoevsky's 'Crime and Punishment' (with some things added):
1. Talk about trivialities in a way which suggests hidden meaning and knowledge of treacherous activities. The suspect becomes scared, and it increases suspense. (Unfortunately, this is much more effective if you're in the accused's POV.)
2. Talk about something else entirely, something unconnected to the whole situation that the suspect cares about and is knowledgeable about. He'll rejoice in talking about it, relieved that it appears as if he hadn't been found out.
3. Out of the blue, hit him right in the face with a blunt question. Stare at his face. For instance, 'he turned sharply, looking into his face, "Why did you sell information to X?"' The reaction and facial expression should be very revealing. Or even better, have someone hidden in the interrogation room, with a view on the suspect's face. The interrogator can then talk to the suspect without looking at him, so the suspect will let his defence down and his reaction to the questions will be even more revealing.
4. Apply pressure, ask questions. Try to fool him by suggestively asking him things he couldn't possibly know if he weren't the traitor. For instance, let's assume the suspect frequented a certain location. It's assumed that information had been given away to a spy on Saturday evening in that location. The suspect of course denies to have been there Saturday, yet freely admits to have been there Friday (because there might have been witnesses, and why should he withold information that doesn't discredit him, this would just make him more suspicious). So now, ask something like 'when you were there on Friday, did you see how the fakir outside was performing his tricks?' In fact, the fakir was only there on Saturday, and in order to sound trustwhorty, the suspect might admit it, mistakenly merging memories and inconspicuously thinking it was Friday when the fakir was there. If the suspect agrees to having seen the fakir, and even adds details, then you caught him lying!
5. Once he admits to having sold secrets, just threat him, and grant him less severe punishment if he tells the whole story. He should be psychologically crushed by now from all the intimidating questions anyway.