appendChild

var rowNr = 1;
function addRow(){
var table = document.getElementById("theTable");
var row = document.createElement("tr");

var first_td = document.createElement("td");
first_td.innerHTML = "Row number: ";

var second_td = document.createElement("td");
second_td.innerHTML = rowNr;

rowNr++;

row.appendChild(first_td);
row.appendChild(second_td);
table.appendChild(row);
}

<table id="theTable">

</table>
<button onClick="addRow();">Add new row</button>

Výsledek skriptu: