What you've described is the older Wordpress way of doing it... If you want to use the new uploader in Wordpress 3.5+, you can create a wp.media object to upload it, similar to the code in wp-admin/js/custom-background.js:

           // Create the media frame.            frame = wp.media.frames.customBackground = wp.media({                // Set the title of the modal.                title: $el.data('choose'),                // Tell the modal to show only images.                library: {                    type: 'image'                },                // Customize the submit button.                button: {                    // Set the text of the button.                    text: $el.data('update'),                    // Tell the button not to close the modal, since we're                    // going to refresh the page when the image is selected.                    close: false                }            });            // When an image is selected, run a callback.            frame.on( 'select', function() {                // Grab the selected attachment.                var attachment = frame.state().get('selection').first();                // Run an AJAX request to set the background image.                $.post( ajaxurl, {                    action: 'set-background-image',                    attachment_id: attachment.id,                    size: 'full'                }).done( function() {                    // When the request completes, reload the window.                    window.location.reload();                });            });            // Finally, open the modal.            frame.open();

the frame.on('select' function(){ code is run when a file is chosen.

A litter further searching and I was able to find some good sources explaining how to do this. I went for a JavaScript, PHP mix:

JavaScript

$j('input').live('focusin',function(){    var target = '#'+$j(this).attr('id');    tb_show('','media-upload.php?post_id=[post_id]&tab=gallery&context=choose&TB_iframe=1');    window.send_to_editor = function(html) {                    fileurl = $j(html).attr('href');        $j(target).val(fileurl);        tb_remove();    };});

source: http://jaspreetchahal.org/wordpress-using-media-uploader-in-your-plugin/

PHP

/* Customize button */function media_uploader_btn($form_fields, $post) {    $send = "<input type='submit' class='button' name='send[$post->ID]' value='" . esc_attr__( 'Choose This File' ) . "' />";    $form_fields['buttons'] = array('tr' => "\t\t<tr class='submit'><td></td><td class='savesend'>$send</td></tr>\n");    $form_fields['context'] = array( 'input' => 'hidden', 'value' => 'choose' );    return $form_fields;}/* Check for button context */function check_upload_image_context($context){    if(isset($_REQUEST['context']) && $_REQUEST['context'] == $context){        return true;    } elseif(isset($_POST['attachments']) && is_array($_POST['attachments'])){        /* check for context in attachment objects */        $image_data = current($_POST['attachments']);        if (isset($image_data['context']) && $image_data['context'] == $context ){            return true;        }    }    return false;}if(check_upload_image_context('choose')){    add_filter('attachment_fields_to_edit', 'media_uploader_btn', 20, 2);}

source: http://shibashake.com/wordpress-theme/how-to-hook-into-the-media-upload-popup-interface