This is an extension (excuse the pun) of elclanrs' solution to include detail on instance methods, as well as taking an extensible approach to that aspect of the question; I fully acknowledge that this is put together thanks to David Flanagan's "JavaScript: The Definitive Guide" (partially adjusted for this context).  Note that this is clearly more verbose than other solutions, but would probably benefit in the long-term.
First we use David's simple "extend" function, which copies properties to a specified object:
function extend(o,p) {
    for (var prop in p) {
        o[prop] = p[prop];
    }
    return o;
}
Then we implement his Subclass definition utility:
function defineSubclass(superclass,     // Constructor of our superclass
                          constructor,  // Constructor of our new subclass
                          methods,      // Instance methods
                          statics) {    // Class properties
        // Set up the prototype object of the subclass
    constructor.prototype = Object.create(superclass.prototype);
    constructor.prototype.constructor = constructor;
    if (methods) extend(constructor.prototype, methods);
    if (statics) extend(constructor, statics);
    return constructor;
}
For the last bit of preparation we enhance our Function prototype with David's new jiggery-pokery:
Function.prototype.extend = function(constructor, methods, statics) {
    return defineSubclass(this, constructor, methods, statics);
};
After defining our Monster class, we do the following (which is re-usable for any new Classes we want to extend/inherit):
var Monkey = Monster.extend(
        // constructor
    function Monkey() {
        this.bananaCount = 5;
        Monster.apply(this, arguments);    // Superclass()
    },
        // methods added to prototype
    {
        eatBanana: function () {
            this.bananaCount--;
            this.health++;
            this.growl();
        }
    }
);