A good place to begin is with the most obvious dialogue. It doesn’t need to be subtle. Write on the nose.
Let your characters go. Then just sit back and watch. It isn’t just what they say. It is also what they do while they talk.
Next, work out what they are hiding. Characters will always hide their true meaning behind their words. Subtext is important.
Learn from the masters. Watch a politician evading questions. Politicians can never be seen to be losing. Someone else is always to blame. They believe themselves to be the masters of deception. As if!