Quick answer: 1500 calories a day, and LOTS of protein to keep hunger away. No exercise beyond such activity as day-to-day life demands.
More details. If you've ever watched "My 600 Pound Life", you know that many of them go for bariatric surgery, but before they do, they have to go on a low-calorie diet and show that they can take off some pounds. And an impressive number of them manage to take off weight pretty rapidly. So, if they can do it in preparation for surgery, why can't the rest of us try a similar diet?
They say an average man needs 2500 calories a day, and a woman needs 2000 calories a day, just to keep their weight stable. In theory, the arithmetic is simple: consume more than that and you gain weight, consume less than that and you lose weight. So how do you consume significantly less than the amount you "should" need, without being constantly hungry?
Fortunately, there are two things you can exploit:
1) Protein takes a long time to digest / metabolize and will keep you feeling full for a longer time than fat or carbs, and
2) your body's hunger signals are flexible and can be trained (or so it seems anyway).
So, for a while now, I've been consuming 1500 calories a day -- or making that my target, at least -- and getting as many of those calories as possible from protein. And the pounds have been dropping off! Yes I'm still tempted by foods, but most days I'm not hungry, and temptation pretty reliably fades away when I remember that I am pulling my belt another notch tighter. (There are some days when I'm hungry -- protein or no, 1500 calories is pretty extreme and it takes its toll -- but on those days, taking it up to 2000 calories or even the "normal" 2500 calories fills me up and I can try for 1500 the next day.)
The first couple days, I wasn't hungry exactly, but my body felt like it was in distress, and I was constantly tired. But by about the third day, I started feeling normal again, and have felt normal since. I think my body eventually figured out that the food availability situation had changed, and started turning to fat reserves rather than demanding traditional caloric intake. This is what I mean when I say that the body's hunger signals seem to be flexible.
I manage my meals in 250-calorie chunks, six of them a day. That way I can do three even meals of 500 calories, or a heavier breakfast of 750 calories, or whatever fits into the day best. So what am I eating? Here are some food options that are roughly 250 calories (yes you WILL become a compulsive calorie-counter):
A variety of lunchmeats fall into this high protein / low calorie territory too -- chicken, turkey, and ham for example.
Beyond that, eat all the vegetables you want, and make plenty of use of sugar-free snacks and beverages. And if it turns out that, by the end of the day you're still full but you've got 500 calories to go, take those 500 calories in any form you like.
Note that I am not recommending exercise. Exercise is good for a great many things -- but when it comes to weight loss, the main thing exercise does is make you hungry. At least in my experience, exercise is the enemy of weight loss. For many of us, taking off the pounds is the most important thing, so do that first, and THEN make exercise your priority. (That said, as weight has come off, I have found that I can walk farther, walk up stairs more easily, etc; so my range of physical activity is inadvertently increasing as I find myself capable of more. Which is ultimately the point!)