How to put on weight?

Some are just naturally small and thin...everything's relative.

Even so, there are protein diets that are good for putting on mass.
I'd recommend finding the special diets that actors use to gain for roles. (they are set up to be safe and healthy)

 

With the lack of exercise, it sounds like "put on weight" means "gain fat."

Is that the case?

If not, GS is mostly right, but you need more than high protein. You need high calories. You need to add 500 or more calories to your average daily intake. Focus on adding foods with caloric density: nuts, seeds, avocados, etc., in addition to more protein. Consider adding a bunch of whole grains too.

As for heavy things, look into weight gain programs focused on big movements such as squats, deadlifts, bench presses, and dumbbell rows. Too much of the wrong kind of lifting could be counterproductive. Sometimes less is more. Focus on the big stuff, leave out the rest.

As a woman, don't worry about "looking too muscly." It's extremely difficult for women to look "mannish" from weight training. Those who do are likely going out of their way to great lengths. Women who are no stranger to resistance training often have impressive physiques that in no way deviate from a feminine figure. Lifting weights will put on muscle where it counts, and your weight will go up if you already have a low body fat percentage. If you already have a low muscle mass, your body fat percentage may be deceptively high ("skinny fat"). Lifting weights with rectify this as you put on more weight.

 

I've heard good things about this book: NROL for Women — The New Rules of Lifting > New Rules of Lifting > Get Lean, Get Strong, Build Muscle. The men's version is pretty good.

Your best asset is decent knowledge. There is a lot of crap out there.