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});

      }

   }

});