Getting a better understanding of callback functions in JavaScript

You can just say

callback();

Alternately you can use the call method if you want to adjust the value of this within the callback.

callback.call( newValueForThis);

Inside the function this would be whatever newValueForThis is.

You should check if the callback exists, and is an executable function:

if (callback && typeof(callback) === "function") {
    // execute the callback, passing parameters as necessary
    callback();
}

A lot of libraries (jQuery, dojo, etc.) use a similar pattern for their asynchronous functions, as well as node.js for all async functions (nodejs usually passes error and data to the callback). Looking into their source code would help!