I too wanted to add this button to the right of the page, had problems moving the iframe so that is was visible so instead decided to open the send button in a dialog window. http://developers.facebook.com/blog/post/514/
You will need to use the JS SDK to do this, and also provide a button or a link that will trigger the send dialog to open. Here is some example code to make a link look like a send button
HTML
<a class="fb-send-button"><i></i><span>Send</span></a>
CSS
.fb-send-button {
-moz-border-radius: 3px;
-webkit-border-radius: 3px;
-o-border-radius: 3px;
-ms-border-radius: 3px;
-khtml-border-radius: 3px;
border-radius: 3px;
cursor: pointer;
color: #3b5998;
-moz-outline-style: none;
text-decoration: none;
background: #eceef5;
border: 1px solid #cad4e7;
display: inline-block;
padding: 4px 5px;
white-space: nowrap;
padding: 2px 5px;
font-family: 'trebuchet ms', sans-serif;
font-size: 11px;
}
.fb-send-button:hover {
border-color: #9dacce;
text-decoration: none;
color: #3b5998;
}
.fb-send-button span {
line-height: 14px;
line-height: 13px;
}
.fb-send-button i, .fb-send-button img {
float: left;
height: 14px;
margin-right: 3px;
width: 14px;
}
.fb-send-button i {
background-image: url(http://static.ak.fbcdn.net/rsrc.php/v1/z7/r/ql9vukDCc4R.png);
background-position: -1px -47px;
}
Javascript
FB.ui({
method: 'send',
name: 'Facebook Dialogs',
link: 'https://developers.facebook.com/docs/reference/dialogs/'
});
You will need to already have the Javascript SDK loaded on your page, and will need to either put the above JS in the anchor tag in an on click attribute, or preferably adding it using your own Javascript.