You don't need to use any server-side code to add a row. The gridview is rendered as a html table by default, so your JavaScript just needs to add another tr, usually at the bottom, such as this
function AddRow()
{
$("#tableID").append("<table><tbody><tr><td>Fill in as necessary<table><tbody><tr><td></td></tr></tbody></table></td></tr></tbody></table>");
}
Reading the data could be like this
function ReadValues()
{
$("#tableID td").each(function()
{
});
}
Using an AJAX method to add or read data from a GridView won't work since the AJAX call is out of band and the GridView is a server control which needs the ASP.NET page lifecyle to reconstitue it from page data or view state.