The quick answer is to use innerHTML (or prototype's update method which pretty much the same thing). The problem with innerHTML is you need to escape the content being assigned. Depending on your targets you will need to do that with other code OR
in IE:-
document.getElementById("field_name").innerText = newText;
in FF:-
document.getElementById("field_name").textContent = newText;
(Actually of FF have the following present in by code)
HTMLElement.prototype.__defineGetter__("innerText", function () { return this.textContent; })
HTMLElement.prototype.__defineSetter__("innerText", function (inputText) { this.textContent = inputText; })
Now I can just use innerText if you need widest possible browser support then this is not a complete solution but neither is using innerHTML in the raw.