It's important to know what to eat to remain healthy. Eating good foods is a good starting point, along with reading nutrition labels.
Cutting fat from the diet isn't enough. First, know about the types of fats, because some can make you healthy, and some can make you extremely ill.
Answer the question of how to increase weight with a methodical approach and proper goal setting: aim to increase lean muscle mass and not body fat.
Losing fat is actually reducing body fat by way of adipose tissue, but how did we become fat in the first place?: carb addiction.