How to document ECMA6 classes with JSDoc?

Late answer, but since I came across this googling something else I thought I'd have a crack at it.

You've probably found by now that the JSDoc site has decent explanations and examples on how to document ES6 features.

Given that, here's how I would document your example:

/**
 * module description
 * @module MyClass
 */
 //constants to be documented. 
 //I usually use the @const, @readonly and @default tags for them
/** @const {String} [description] */
const CONST_1 = "1";
/** @const {Number} [description] */
const CONST_2 = 2;

//An example class
/** MyClass description */
class MyClass {

    //the class constructor
    /**
     * constructor description
     * @param  {[type]} config [description]
     */
    constructor(config) {
        //class members. Should be private. 
        /** @private */
        this.member1 = config;
        /** @private */
        this.member2 = "bananas";
    }

    //A normal method, public
    /** methodOne description */
    methodOne() {
       console.log( methodThree("I like bananas"));
    }

    //Another method. Receives a Fruit object parameter, public
    /**
     * methodTwo description
     * @param  {Object} fruit      [description]
     * @param  {String} fruit.name [description]
     * @return {String}            [description]
     */
    methodTwo(fruit) {
        return "he likes " + fruit.name;
    }

    //private method
    /**   
     * methodThree description
     * @private
     * @param  {String} str [description]
     * @return {String}     [description]
     */
    methodThree(str) {
       return "I think " + str;
    }
}
module.exports = MyClass;

Note that @const implies readonly and default automatically. JSDoc will pick up the export, the @class and the @constructor correctly, so only the oddities like private members need to be specified.

For anyone visiting this question in 2019:
The answer given by @FredStark is still correct, however, the following points should be noted:

1. Most/all of the links in this page are dead. For the documentation of the JSDoc, you can see here.
2. In many IDEs or code editors (such as VSCode), you will find auto-completions such as @class or @constructor which are not necessary for the case of ES6 classes since these editors will recognize the constructor after the new keyword.