So, you want to increase weight, but not fat?
Well, it's not too tough, but it's not too simple, either, and it'll require that you put in some honest physical effort aside from simply changing your eating plans

First this is first: Realize that excercise alone will do nothing for you. Just the same, diet alone will do nothing for you. Both are meant to supplement the other. Your diet is the fuel to power you through a bit of daily excercise, which can keep you going for a long, long time, as I've seen. So, treat it as such; think of yourself as a car. You can't run on empty for too long, can you? Just as well, if I put sugar in your car's tank and nothing else, it'd probably make you more than a bit late for work in the morn' ;)
A basic diet should balance out the major "food groups," as noted by the US government. While I don't agree with the 2,000 calories per-day guidelines, as they are too strict, and account for only the "average" body, which is also determined by the government, in accordance with survey data, the FDA, etc.
There is an obvious step to increasing muscle (or "lean") mass, and that is to increase your intake of protein. However, as you do this, you also need to increase your intake of carbohydrates -- complex carbs, such as those you find in raw pastas, multi-grain breads (which are also a good primary source for fiber), rather than "simple carbs," which you may find in mashed 'taters.
In essence, don't simply increase your intake of one type of food, while you allow for others to remain the same. See all of those extra-chunkeh football players? Many of the larger ones have been proven to use things like "Whey Protein" incorrectly. Too much protein in your system = fat.
So, if you're going to increase your protein intake, you need to also increase your intake of dark, leafy greens, to help speed up your metabolism just a bit. Excercise will supplement this speedy metabolic rate, and allow you to make the best use of the protein you consume, so that the vast majority of it goes to aiding your muscles in their growth, rather than becoming fat to be stored in the subcutaneous layer of your skin, and to smother your interal organs.
Google is your friend for discovering which greens, lean meats (such as fish, and poultry -- beef is considered a red meat, and should be eaten in smaller proportions, and less often, for maintaining a certain level of health), and grains you should/could eat to keep your body in good shape. Try looking up a few. I'd do so, but I'm trying to keep this short, and sweet

Pay attention to
how you eat. The ideal consumption of food should come in smaller portions, 5-6 times per day, if you can manage. Consuming food in this way, rather than in large portions at three sittings, allows for you to keep your body properly nourished throughout the day, without over-stuffing yourself, as the average american does! When you eat large proportions you are only pushing more food which will not be used into your body, and so it sits, and becomes fat. That's the american way, though, and it's tough to break. The 5-6 meals-a-day method keeps your energy levels up without stuffing you so that you become sloth-like. You should never feel "absolutely full." It's ideal that your body always be craving more energy, though you don't need to be starving, either.
The object of losing weight is to burn more calories than you take in. For keeping your "figure," while increasing muscle mass, this rule remains generally the same. The amount of calories you burn should be greater than the amount you take in, but it's the
type of calories you take in that count. Your body needs carbs to keep going; if it lacks these essential fuels, then it will resort to eating its own muscle, and before you know it you WILL lose weight, but it will be muscle, not fat, which is not good.
If you cannot eat 5-6 times per day, don't fret! Eating three medium-sized meals is never a bad thing. You simply need to watch what you eat. Try to balance your meals with a healthy sampling of meats, greens, fibers, carbohydrates, etc. etc. etc. If you can, drink milk, or supplement Vitamin A, B, C (which has been known to increase and maintain speedy metabolic rates), D, and so on. A health dose of iron, and zinc should also be present. You can obtain all of these through multi-vitamins. Just run down to the local health-food store, Wal-mart, Drug-store, or any place that supplies this sort of thing and look over some labels. I take a multi-vitamin each day for my own health.
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Exercise: Don't forget this. A good 30 minutes of cardio per day should be a healthy start. As you increase your physical capability, you can begin to include weights -- you should never JUST lift weights without any cardio thrown in the mix, as it's not healthy for your heart (endurance) -- and also begin to extend the time that you excercise for each day. Everything comes in small increments, though, so keep your safety in mind. After-all, you're eating good and excercising to be healthy, right?

This is a pretty basic -- very, very basic -- summary of the platform for your healthy start, I think. Lots of info is left out, though, so google your heart out. Remember, though, take everything with a grain of salt. It's probably
best to consult a doctor before making serious dietary or lifestyle changes. On the net, anyone can say anything.
Ang