The bare minimum required to meet essential nutrient intake is 1200 through natural food alone. obviously sythesised nutrient intake (pills etc) can reduce this but whether pills are any good is unproven.
you need to create a weekly deficit of 3500 to lose 1lb of fat. now look at the following two statements carefully and think about what your first answer would be.
1. to lose weight i must consume less calories than i burn.
2. to lose weight i must burn more calories than i consume.
now i'm betting 1. you think diet. and 2 you think exercise. this is a simple trick of the english language both statements are correct and mean the same thing. however no 1 is generally promoted to females via magazines and infomercials. and no2 is generally promoted to males via the same mediums.
but what they don't tell you is burning more than you need is better than consuming less. when you exercise your metabolism is increased during the exercise this burns calories. (ok you know this) but when you finish exercise your metabolism doesn't instantly return to base rate. it takes hours thats right hours to return to base level. so the treamill says you only burnt 100 calories on that walk but over the next 3 hours you may well burn 100 more than base as the metabolism gradually slows down.
if you cut your intake initially you lose weight. however after a shockingly short period of time the metabolism starts to slow down to the new energy intake level this is why your weight loss slows and you eventually stop losing weight. if you run at 1200 calories a day you will eventually adapt to 1200 calories a day. this is your plateau.
at your plateau you are now back at square 1. you have to resort to the above 2 statements again. if you come off your "diet" and revert to old habits. (hand up here guilty, many many times over) but if your body is adapted to 1200 a day and you suddenly go back to 1400 then 1500 etc with junk and fast food you will put weight on and the body annoyingly takes longer to build up its metabolism than slow it down.
Bottom line raise amount of energy used not the amount you consume its the best way all round..

. The end result of a healthy, maintainable loss is the goal, however you choose to get there.