Some mental factors (processes) are the link between cognition and emotion - such as basic imagery (body images), thoughts, and other cognitive associations and structures.
How exactly does the mind 'think' however? I could say that it uses images to think, and that these images are mostly unconscious. That would be similar to having a dream, in a dream simple images represent larger psychological ideas and life experiences. The images your mind uses to think are probably basic, similar to how a computer works with simple switches at the most simple level. The most basic and important mental images are used to represent more significant psychological 'code' or life experiences (like body images - since social interaction is important humans would be broken down in the mind into simple visualizations).
So I think that the mind basically thinks by breaking down the psychological factors of life into more simple images. If you have an interaction with someone, then that interaction is broken down into more simple body-images and other images that represent what occurred in the interaction. These images are probably unconscious, you would not notice in what order your mind is going through them or what they are exactly.
This means that your minds cognitions (such as images and thoughts) are going to influence your emotions. The real world is broken down into thoughts and visualizations (or psychological 'symbols') in your mind, and these mental processes influence your emotions.