Shift from the role of writer to that of actor. Become your character. Say out loud what that character would say as s/he would say it. It might help to use a DVR and record your role-playing. Now, play back. Listen to you taking on the characters and saying the lines. Do they sound right? Natural? Are they appropriate to the character and the scene? Is the emotion right?
As we've gotten away from so many he-said-she-said tags, action beats are almost a part of the dialogue. To get them right, you might have to get up and act out the scene. Be aware of your facial expressions, your body language, your body positioning, how your character moves through the scene and relates to the other characters. Capture that on the page, leaving out the unimportant details your reader can intuit.