Best practices for static methods and variables with MooTools classes

Caveat: Never used MooTools. I've used Prototype a fair bit, though, which has a similar Class system (MooTools is either "inspired by" or a fork of Prototype, depending on who you ask).

Just add them as properties on the resulting "class":

var MyClass = new Class(properties);
MyClass.staticMethod = function() {
    // ...
};

(The first line above is from the docs; the remainder is my addition.)

You know that will happen prior to initialize on any new instance because you're not leaving an opportunity for creating a new instance prior to attaching your static methods (or properties).

I know this post is old, but I wanted to give a better answer than was already stated.
I recommend the following syntax for static methods:

var MyClass = new Class({
    initialize: function() {
        this.method();
        MyClass.staticMethod();
    }
    ,
    method: function() {}
}).extend({
    staticMethod: function() {}
});

The .extend({}) method is the standard way to add static methods on a Class.

The only thing I don't like is the MyClass.staticMethod(); syntax, but there aren't many better options.