Reorganizing the code, you could use something like this:
(function () {
"use strict";
var counter, init, addWorkshop, renameInputs, removeWorkshop;
counter = 0;
init = function () {
document.getElementById("moreWorkshops").onclick = addWorkshop;
addWorkshop();
};
addWorkshop = function () {
var clonedWorkshop, targetInsert;
counter++;
clonedWorkshop = document.getElementById("readroot").cloneNode(true);
clonedWorkshop.id = "";
clonedWorkshop.className = "";
clonedWorkshop.querySelector(".remover").onclick = removeWorkshop;
renameInputs(clonedWorkshop);
targetInsert = document.getElementById("writeroot");
targetInsert.parentNode.insertBefore(clonedWorkshop, targetInsert);
};
renameInputs = function (container) {
var children, i, j, cur, theName;
children = container.children;
for (i = 0, j = children.length; i < j; i++) {
cur = children[i];
if (cur.nodeName.toLowerCase() === "input") {
theName = cur.name;
if (theName) {
cur.name = theName + counter;
}
} else {
renameInputs(cur);
}
}
};
removeWorkshop = function () {
this.parentNode.parentNode.removeChild(this.parentNode);
};
window.onload = init;
}());
DEMO: http://jsfiddle.net/gAaxS/
Note that this is very structure-specific - for example, the this.parentNode.parentNode
means that it has exactly two ancestors that you want to target. If you changed the HTML, you'd have to change the JS (which is usual).