Is it as simple as calories in < calories out

Yes it is - it really is that simple..... If anyone tells you this isn't the case I don't think they have grasped the basics. But things are not quite as simple as they seem....

calories in can be calculated very easily just by adding what you eat up.
calories out is difficult. From my understanding Cals out = BMR (just the calories used to keep your body running if you lay in bed all day) + exercise cals but both of these can vary. They both depend upon weight but they also depend upon your body composition, what you are doing to your body and how well your body is holding to any stresses (or lack of stresses) you are giving it.

for me the complexities are too much so I need to simply things - For instance I don't know (no one does without hooking me up to some complex test equipment) what my BMR is . Similarly I don't know for sure how many calories my body burns when i exercise. BUT, and this is the good bit, MFP guesses these for you. After reading some posts from the people who put this together they have made some assumptions about what YOU are going to do - if you stick to these the programme will most probably. calculate your weight reduction quite accurately. These assumptions are that you keep your body hydrated (hence the water level you can input) and that you loose weight at a rate of no more that 2lb per week. For instance increasing a weight loss over for a few days or weeks according to the site techs research can reduce your BMR. If you stick to these two rules then you will be well on your way. when you start off though your body will reconfigure itself over the first few weeks - it can loose water and gain muscle so weight is not really a good short term measure of how you are doing as it can reduce drastically or even go up a bit - but after this initial period and then over a few months you should notice that your weight drops a certain amount each week as long as you are burning calories . If after a couple of months you notice week on week that the guess made by MFP is out (i.e. it says 2lb loss and you get 1.5 lb loss (repeated over a few weeks) it means that MFP isn't quite predicting accurately for you (we are all different and MFP will no doubt be programmed for ms/mr average) . You could if you so wish manually adjust the cals in/calls out per day to change your real loss to your target loss (in the case of 1/2 lb difference you would need to adjust your cals by (3500*1/2 )/ 7 per day. Again if you are bulking out your muscle MFP wont know this and then the scales may not go down fast but that is because some parts of you are increasing in size :-) In general though by listening to a load of people for those who are only loosing weight and exercising without deliberately bulking MFP seems to be predicting accurately enough for them to be losing weight at a comfortable and acceptable level. .

Short answer: Yes.

Slightly longer answer: No, but 99% of people who give reasons why it isn't are completely wrong about why. 90% of weight changes can be explained by raw calories in/calories out. 90% of the remaining 10% is explained by thermic effect of food.

Yes, it pretty much is that simple. If you don't over eat then your body isn't going to have the fat to store to make you fat. Can't comment on how many calories you should have, though. I'm very thin and can maintain my weight eating around 1650 daily and I don't "exercise", I just walk daily. Everyone's body is different. Tracking your calories over time is a way to get an idea of just how much you need to be eating.