How can I create and use a Javascript class in a PhotoShop script?

ExtendScript is ES3, doesn't implement class keyword as does ES6 used by most browsers now. From what you describe, it doesn't seem you even need a class. If you want to store a collection of variables just make an object to store it.

person = {
  name: "Joe",
  age : 30,
  gender: "male"
};

Then to use...

var gender = person.gender;

It's possible, but not in the way you might want/think...

As Kukurykus said, ExtendScript is about 20 yrs old and something called a Class isn't available, at least, the keyword Class doesn't mean much.

This is a way to make something that behaves like a class:

(function() {
    this.MyClass = (function() {
        int prop1 = 0;
        function MyClass(param) {
           prop1 = param; 
        };

        MyClass.prototype.MyFunction = function(param1, param2) {
            prop1 = param1;
            return param2;
        };
        return MyClass;
    })();
}).call(this);

This part --> (function(){/*... the 'class' content...*/}).call(this);  turns an anonymous function into a "class.

And here's an example of how you would call it:

#include "./somefolders/MyClass.jsx";
var MyScript = (function() {
    var HoldMyBeer_Instance = "HoldMyBeer will be an instance of MyClass... (sort of.)";

    function constructor() {
        HoldMyBeer_Instance = new MyClass(5);
    };

    constructor.prototype.MyThing = function() {
        return HoldMyBeer_Instance.MyFunction(1,2);
    };
    return constructor;
})();

No need to explain the include part, you already got that. 🙂

You can think of The MyScript variable as the Program class in other languages.

In function constructor(){...}, constructor is an arbitrary name, not a reserved keyword.

To attach methods/properties to your class, use constructor.prototype.nameofyourthing = ...

In the example, in MyThing() will call the function MyFunction of the instance of our data class.

ExtendScript uses old implementaion from about 20 years.