[jquery] assign function return value to some variable using javascript

The only way to retrieve the correct value in your context is to run $.ajax() function synchronously (what actually contradicts to main AJAX idea). There is the special configuration attribute async you should set to false. In that case the main scope which actually contains $.ajax() function call is paused until the synchronous function is done, so, the return is called only after $.ajax().

function doSomething() {
    var status = 0;
    $.ajax({
        url: 'action.php',
        type: 'POST',
        data: dataString,
        async: false,
        success: function (txtBack) {
            if (txtBack == 1)
                status = 1;
        }
    });

    return status;
}

var response = doSomething();