It is not appealing to have extra breast fat, but loosing it is not much of a problem. All you have to do is to loose some weight, to do a couple of adequate exercises, and not to loose the will to see it through. Yeah, I can almost hear you say "Right, piece of cake". But long-term results will certainly make it worth your while.
Exercises can not be aimed at loosing fat from the breasts alone. It does not work that way. You can focus on a muscle or muscle group, work that out, and see it become bigger and stronger. But that is how muscles operate. Fat is a different matter. It tends to accumulate in some places more than others, but when you need some extra energy, it gets drawn from all over the body, not just from places nearest to muscle(s) that are asking for extra fuel. Downside of this is that there is no quick fix method for excess fat anywhere, but that you must work on overall accumulated fat.
Then again, who would not want to get rid of excess fat from everywhere? It will just be obvious on the wrong place a bit longer and nothing more. But you will be satisfied with system-wide loss of excess fat, won't you? Exercising the upper body won't burn breast fat specifically, but will help to tone and improve the overall appearance of the region and thus make the excess fat less prominent. Remember to work out all muscles evenly.
Cable chest press is done on a home workout machine or in the gym. It helps to tone and strengthen pectoral muscles, which can pull up on breast and make any excess less obvious. Do as many reps of ten pulls as you can until you feel fatigue, and don't pull too much weight. You are trying to burn fat there, not to make your name in bodybuilding. This exercise can be improvised with free-weights. Motion is similar; you just need to be lying down instead of sitting.
Bench pressing improves tone of pectoral muscles and various shoulder muscles. This exercise can also be improvised at home, but you will need heavier free-weights than those used for arms alone.
True diet is not tough. It is all about gradual and permanent change of your eating habits. When done in such a way, it is not stressful and permanent moderation of what you eat also brings permanent effects. Key in both exercising and adhering to a diet is to persist. Do it regularly and it will work. Do it occasionally and it will fail.