OnClick without jQuery

When this anchor will contain only one function to handle on click, than you can just write

document.getElementById('anchorID').onclick=function(){/* some code */}

otherwise, you have to use DOM method addEventListener

function clickHandler(){ /* some code */ }
var anchor = document.getElementById('anchorID');
if(anchor.addEventListener) // DOM method
  anchor.addEventListener('click', clickHandler, false);
else if(anchor.attachEvent) // this is for IE, because it doesn't support addEventListener
   anchor.attachEvent('onclick', function(){ return clickHandler.apply(anchor, [window.event]}); // this strange part for making the keyword 'this' indicate the clicked anchor

also remember to call the above code when all elements are loaded (eg. on window.onload)

-- edit

I see you added some details. If you want to replace the code below

$("a.scroll-up, a.scroll-down").click(function(){SNavigate($(this).attr("href").substr(7));return false;});

with sth that doesn't use jQuery, this should do the job

function addEvent(obj, type, fn) {
        if (obj.addEventListener)
                obj.addEventListener(type, fn, false);
        else if (obj.attachEvent)
                obj.attachEvent('on' + type, function() { return fn.apply(obj, [window.event]);});
}
addEvent(window, 'load', function(){
   for(var i=0, a=document.anchors, l=a.length; i<l;++i){
      if(a[i].className == 'scroll-up' || a[i].className == 'scroll-down'){
         addEvent(a[i], 'click', function(e){ SNavigate(this.href.substr(7)); e.returnValue=false; if(e.preventDefault)e.preventDefault();return false});
      }
   }
});

how about this :

document.getElementById("lady").onclick = function () {alert('onclick');};

W3C suggests:

element.addEventListener('click',doSomething,false)

Microsoft uses:

element.attachEvent('onclick',doSomething)

You can do some feature detection and determine which call to use.

From http://www.quirksmode.org/js/events_advanced.html.