Regarding fats: while they are more than double the energy density per gram than protein or carbohydrate (9 cals. vs 4), they're also far more satiety-promoting. In other words, if you're filling up on fats, you're getting calories, but not necessarily the ones you may need to start building useful new tissue. Obviously zero fat is crazy (and unhealthy!), not to mention it makes things taste awful, but try to avoid the temptation to just suck down a lot of fat. You'll feel too full to get much of anything else!
In sort do the opposite of what people do for weight loss. I am assuming you want to do it in a healthy way.
Drink your calories. Milk, protein shakes help with this.
Eat highly caloric food. Add oil, butter to things.
Eat easily digestible food. White rice, ground beef.
Eat faster, so your body doesn't realize you are no longer hungry.
White chocolate works well similarly; hard to find unsweetened but that can work with a lot of dishes.
I'm clawing to stay above 100lb; digestive troubles. Interested in others tips as well; its not the common question.
Being at a particular weight is not inherently healthy (though it may be healthier than some other weight levels)**. Health and fitness objectives are better for long term sustainment. If I wanted to weigh 250 pounds, I could do it very easily. I'd eat a pint of ice cream a day, drink a few glasses of milk a day, drink sugary drinks again, and stop exercising. But that's not healthy. Same for anything between my current weight (190lbs) and a random higher target weight.
The next question is, how do I stop gaining weight and then maintain that particular weight? That's a harder thing to do than you might think. At 250lbs, I could shed (based on past experience) 30lbs just by cutting out the ice cream and sodas, before cutting out the milk and adding back exercise. Buying a few gallons of milk a week isn't cheap, same with ice cream and sodas, so it would be easy for me to lose some of the weight just by seeing the grocery bills and wanting to spend money on useful things instead.
To the extent that I "plan" to gain weight, it's going to be a side-effect of a separate goal: Getting stronger. I'm currently doing some other training, but by the end of March or beginning of April (at the latest) I plan to start weightlifting again (haven't done it in years at this point). From past experience, I will put on 10-20 pounds in about 3 months. I'll have to eat more during that time, but my weight will settle around 200lbs if it goes like in the past and I don't overdo it on the eating. But again weight gain is not my goal, it's a consequence of a specific training effort I plan on doing and strength goals (I have some specific targets in mind on the bench press, in particular, and other exercises will be done to help with chronic back problems).
If I could gain that strength without gaining weight, I wouldn't care, the strength and back health, in my case, are the goals. So what are your goals?
If it's just gaining weight: eat more, move less.
EDIT:
** I didn't quite write what I intended here. If you are obese or severely underweight (possibly due to malnourishment or other health issues) then that's unhealthy. But a "healthy" weight is actually a pretty big range and depends on many factors: age, back and joint health, diet, hereditary concerns, overall fitness level, body composition. My healthy weight without also exercising is in the range of 170-190. With exercising, it depends on the kind of exercising, but ranges from 175 (primarily running) to 210 (weight training).
If I'm inactive, 190-210 are not totally unhealthy, but aren't exactly healthy either (my cholesterol levels start shooting up in that range). Above 210 without exercising and I have trouble with my back and knees, and at my height am at the lower level of obese, and the back and knee problems cause my weight to shoot up higher because I have more trouble with basic mobility (hooray for a compressed disk injury).
So if you're underweight to the point that it's unhealthy, sure you need to gain weight. But you also have to figure out why you're underweight and what to do about it. But the basic process is the same: eat more. You can't gain weight without consuming more calories than your body uses.