How to create a jQuery function (a new jQuery method or plugin)?

In spite of all the answers you already received, it is worth noting that you do not need to write a plugin to use jQuery in a function. Certainly if it's a simple, one-time function, I believe writing a plugin is overkill. It could be done much more easily by just passing the selector to the function as a parameter. Your code would look something like this:

function myFunction($param) {
   $param.hide();  // or whatever you want to do
   ...
}

myFunction($('#my_div'));

Note that the $ in the variable name $param is not required. It is just a habit of mine to make it easy to remember that that variable contains a jQuery selector. You could just use param as well.

From the Docs:

(function( $ ){
   $.fn.myfunction = function() {
      alert('hello world');
      return this;
   }; 
})( jQuery );

Then you do

$('#my_div').myfunction();

To make a function available on jQuery objects you add it to the jQuery prototype (fn is a shortcut for prototype in jQuery) like this:

jQuery.fn.myFunction = function() {
    // Usually iterate over the items and return for chainability
    // 'this' is the elements returns by the selector
    return this.each(function() { 
         // do something to each item matching the selector
    }
}

This is usually called a jQuery plugin.

Example - http://jsfiddle.net/VwPrm/

While there is a plethora of documentation / tutorials out there, the simple answer for your question is this:

// to create a jQuery function, you basically just extend the jQuery prototype
// (using the fn alias)

$.fn.myfunction = function () {
    // blah
};

Inside that function, the this variable corresponds to the jQuery wrapped set you called your function on. So something like:

$.fn.myfunction = function () {
    console.log(this.length);
};

$('.foo').myfunction();

... will flush to the console the number of elements with the class foo.

Of course, there is a bit more to semantics than that (as well as best practices, and all that jazz), so make sure you read up on it.