In order to load a JavaScript file dynamically different methods can be used, here are a few:

Method 1: 

Simply create an include function to handle both script and css files. This function also checks to make sure that the script or CSS file hasn't already been loaded dynamically. 
function include( url, type ){
    // First make sure it hasn't been loaded by something else.
    if( Array.contains( includedFile, url ) )
        return;

    // Determine the MIME-type
    var jsExpr = new RegExp( "js$", "i" );
    var cssExpr = new RegExp( "css$", "i" );
    if( type == null )
        if( jsExpr.test( url ) )
            type = 'text/javascript';
        else if( cssExpr.test( url ) )
            type = 'text/css';

    // Create the appropriate element.
    var tag = null;
    switch( type ){
        case 'text/javascript' :
            tag = document.createElement( 'script' );
            tag.type = type;
            tag.src = url;
            break;
        case 'text/css' :
            tag = document.createElement( 'link' );
            tag.rel = 'stylesheet';
            tag.type = type;
            tag.href = url;
            break;
    }

    // Insert it to the  and the array to ensure it is not
    // loaded again.
    document.getElementsByTagName("head")[0].appendChild( tag );
    Array.add( includedFile, url );
}

Note: "includedFile" and "Array" variables must be defined.

Method 2: 

  var js = ["scripts/jquery.dimensions.js", "scripts/shadedborder.js", "scripts/jqmodal.js", "scripts/main.js"];
  for (var i = 0, l = js.length; i < l; i++) {
  document.getElementsByTagName("head")[0].innerHTML += ("");
  }
Same method using JQuery
  var js = ["scripts/jquery.dimensions.js", "scripts/shadedborder.js", "scripts/jqmodal.js", "scripts/main.js"];
  var $head = $("head");
  for (var i = 0; i < js.length; i++) {
  $head.append("");
  }

Method 3:

Using Jquery getScript Method. 
   $.getScript("my_lovely_script.js", function(){
  // here you can use anything you defined in the loaded script
 });

Method 4: 

Another Simpler Method using plain JS 
function include(url)
  {
    var s = document.createElement("script");
    s.setAttribute("type", "text/javascript");
    s.setAttribute("src", url);
    var nodes = document.getElementsByTagName("*");
    var node = nodes[nodes.length -1].parentNode;
    node.appendChild(s);
  }