The basic function would be this:

string = string.replace(/[^a-zA-Z0-9]/g, '')

This would replace any character that is not described by [a-zA-Z0-9].

Now you could either put it directly into your element declaration:

<input type=text class=alphanumericOnly onkeyup=this.value=this.value.replace(/[^a-zA-Z0-9]/g, '')>

Or (as you used the class hint) you assign this behavior to every input element with the class alphanumericOnly:

var inputElems = document.getElemenstByTagName(input);

for (var i=0; i<inputElems.length; i++) {

    var elem = inputElems[i];

    if (elem.nodeName == INPUT && /(?:^|s+)alphanumericOnly(?:s+|$)/.test(elem.className) {

        elem.onkeyup = function() {

            this.value = this.value.replace(/[^a-zA-Z0-9]/g, '');

        }

    }

}

But it’s probably easier to do that with jQuery or another JavaScript framework:

$(input.alphanumericOnly).bind(keyup, function(e) {

    this.value = this.value.replace(/[^a-zA-Z0-9]/g, '');

});