Gaining weight seems to be the hardest thing ever!

Exercise for gaining weight is up to you but lifting heavy is recommended to maximize muscle gains vs fat gains. As for foods, just eat what you like but more of it than you normally would since you want to achieve a surplus of 250-500 calories per day over maintenance so you will need to determine what that is. To maximize muscle gains you will need roughly .8g of protein per pound of body weight.

Gaining is usually more of an attitude than anything else since you will likely have doubts later on as you put on body fat.

I was always a skinny guy unable to put on weight. I can tell you what worked for me to stay healthy and gain lean weight.

First you have to Google for a TDEE calculator. This will tell you the number of calories you consume with normal daily living. You have to be at a surplus over TDEE. So you add calories to the TDEE and track your calories. You want to make sure you are gaining only a small amount each week or so. This will make sure you are not gaining too much fat. For me, a 300 calorie surplus allowed me to gain .5 to 1 lb. per week. You need to be patient.

You need to make sure you get enough of each macro: protein, carbs and fat. In my case, I made sure to get 40% protein, 40% carbs and 20% fat. You need to eat lean meats (chicken, fish, turkey, lean beef), vegetables, fruits and dairy (yogurt, cottage cheese). It's okay to have things you like too in moderation (pizza, ice cream, cheeseburger, fries) as long as you meet your macro percentages and calorie surplus. It doesn't have to be exact but close each day. Also, adding protein powder with milk or water helps to reach your protein/calorie goal.

It's important to drink sufficient water. I drink at least a gallon of water each day. Most say that 8 glasses of water of day should be a minimum amount to drink. And taking a multi vitamin will ensure that you are getting all of your micronutrients.

Last thing and most important is weight training. There are many weight training sites online that have great workouts for beginners. This will help you to maintain and gain muscle and minimize fat gains. I work out only 3 days a week about an hour per workout. I keep cardio to a minimum to make sure I keep gains from weight training and let my body rebuild and refresh so that I have energy for weight training.

gaining "weight" is easy, gaining lean body mass is difficult (naturally)
to gain LBM as @Wheelhouse15 has said you need to have a calorie surplus, plus do some form of resistance training, plenty of ideas for training exercises on youtube. To keep fat gain to a minimum keep the surplus small to start with, maybe 200-300 cals a day over your maintenance calories, after a few weeks you can *kitten* your progress and adjust your calories if needed.
keep your diet clean as @psulemon has said choose good protein sources.
It will be a slow process, building muscle takes time.

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