Act out your dialogue. Like, seriously act it out. Put on voices, speak with your character's accents, move your body the way they would move theirs, and do that over, and over, and over, and over... With each pass, the scene will get tighter, the dialogue will flow better, and you'll get more of a sense of how your characters stand, move, and how they're feeling.
That's my 'secret sauce' for believable dialogue, and dialogue is something which I'm complimented on frequently, so I'm dead certain it really helps.