Calories Needed to Gain Weight
There are two ways to go about finding how many calories you need to gain weight. The first is to use a formula. A common formula used to determine the number is 18 x BW (lbs). This gives you a good baseline number, but since everyone is different this number could be too low. As you progress, it will take more and more calories consumed to gain weight so this formula will become useless.
The second method, which is the better method, is to use tracking software for a week and see how many calories you are consuming and how much weight you are gaining. So start off with a baseline number, eat that for a week and track your weight and then you will know if it is working or not. If you didn't gain weight or didn't gain as much as you wanted, increase the daily calorie number by 500 and track for another week. unless you are going for extremely fast weight gain, aim for about 1 lb/ week.
If you do want to go for fast weight gain, just eat as much food as you can. This should be at least 4000 kcal a day. It may be difficult to eat this much food, but if you can manage it and be consistent you will gain weight extremely fast. Just a warning though, if you do this, you will gain more fat than with the slower method above.