Jquery If radio button is checked

$('input:radio[name="postage"]').change(
    function(){
        if ($(this).is(':checked') && $(this).val() == 'Yes') {
            // append goes here
        }
    });

Or, the above - again - using a little less superfluous jQuery:

$('input:radio[name="postage"]').change(
    function(){
        if (this.checked && this.value == 'Yes') {
            // note that, as per comments, the 'changed'
            // <input> will *always* be checked, as the change
            // event only fires on checking an <input>, not
            // on un-checking it.
            // append goes here
        }
    });

Revised (improved-some) jQuery:

// defines a div element with the text "You're appendin'!"
// assigns that div to the variable 'appended'
var appended = $('<div />').text("You're appendin'!");

// assigns the 'id' of "appended" to the 'appended' element
appended.id = 'appended';

// 1. selects '<input type="radio" />' elements with the 'name' attribute of 'postage'
// 2. assigns the onChange/onchange event handler
$('input:radio[name="postage"]').change(
    function(){

        // checks that the clicked radio button is the one of value 'Yes'
        // the value of the element is the one that's checked (as noted by @shef in comments)
        if ($(this).val() == 'Yes') {

            // appends the 'appended' element to the 'body' tag
            $(appended).appendTo('body');
        }
        else {

            // if it's the 'No' button removes the 'appended' element.
            $(appended).remove();
        }
    });

var appended = $('<div />').text("You're appendin'!");
appended.id = 'appended';
$('input:radio[name="postage"]').change(function() {
  if ($(this).val() == 'Yes') {
    $(appended).appendTo('body');
  } else {
    $(appended).remove();
  }
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.6.2/jquery.min.js"></script>
<input type="radio" id="postageyes" name="postage" value="Yes" />Yes
<input type="radio" id="postageno" name="postage" value="No" />No

JS Fiddle demo.

And, further, a mild update (since I was editing to include Snippets as well as the JS Fiddle links), in order to wrap the <input /> elements with <label>s - allow for clicking the text to update the relevant <input /> - and changing the means of creating the content to append:

var appended = $('<div />', {
  'id': 'appended',
  'text': 'Appended content'
});
$('input:radio[name="postage"]').change(function() {
  if ($(this).val() == 'Yes') {
    $(appended).appendTo('body');
  } else {
    $(appended).remove();
  }
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<label>
  <input type="radio" id="postageyes" name="postage" value="Yes" />Yes</label>
<label>
  <input type="radio" id="postageno" name="postage" value="No" />No</label>

JS Fiddle demo.

Also, if you only need to show content depending on which element is checked by the user, a slight update that will toggle visibility using an explicit show/hide:

// caching a reference to the dependant/conditional content:
var conditionalContent = $('#conditional'),
    // caching a reference to the group of inputs, since we're using that
    // same group twice:
    group = $('input[type=radio][name=postage]');

// binding the change event-handler:
group.change(function() {
  // toggling the visibility of the conditionalContent, which will
  // be shown if the assessment returns true and hidden otherwise:
  conditionalContent.toggle(group.filter(':checked').val() === 'Yes');
  // triggering the change event on the group, to appropriately show/hide
  // the conditionalContent on page-load/DOM-ready:
}).change();

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<label>
  <input type="radio" id="postageyes" name="postage" value="Yes" />Yes</label>
<label>
  <input type="radio" id="postageno" name="postage" value="No" />No</label>
<div id="conditional">
  <p>This should only show when the 'Yes' radio &lt;input&gt; element is checked.</p>
</div>

And, finally, using just CSS:

/* setting the default of the conditionally-displayed content
to hidden: */
#conditional {
  display: none;
}

/* if the #postageyes element is checked then the general sibling of
that element, with the id of 'conditional', will be shown: */
#postageyes:checked ~ #conditional {
  display: block;
}

<!-- note that the <input> elements are now not wrapped in the <label> elements,
in order that the #conditional element is a (subsequent) sibling of the radio
<input> elements: -->
<input type="radio" id="postageyes" name="postage" value="Yes" />
<label for="postageyes">Yes</label>
<input type="radio" id="postageno" name="postage" value="No" />
<label for="postageno">No</label>
<div id="conditional">
  <p>This should only show when the 'Yes' radio &lt;input&gt; element is checked.</p>
</div>

JS Fiddle demo.

References:

• CSS:
  • :checked selector.
  • CSS Attribute-selectors.
  • General sibling (~) combinator.
• jQuery:
  • appendTo().
  • attribute-equals selector.
  • change().
  • :checked selector.
  • filter().
  • is().
  • :radio selector.
  • remove().
  • text().
  • toggle().
  • val().

Something like this:

if($('#postageyes').is(':checked')) {
// do stuff
}

Try this

if($("input:radio[name=postage]").is(":checked")){
  //Code to append goes here
}

if($('#test2').is(':checked')) {
    $(this).append('stuff');
}