How to use Assets or EE's File Manager anywhere in the CP

example.php

<?php

if ( array_key_exists('assets', $this->EE->addons->get_installed()) )
{
    // Load Assets' assets
    if ( ! isset($this->EE->session->cache['assets']['included_sheet_resources']))
    {
        if (! class_exists('Assets_helper'))
        {
            require PATH_THIRD.'assets/helper.php';
        }

        $assets_helper = new Assets_helper;
        $assets_helper->include_sheet_resources();
    }

    foreach( $fields as $k => $field)
    {
        $script = '$("#thumbnail_trigger_'. $k .'").click(function(e){
            var sheet = new Assets.Sheet({
                filedirs: "all",
                kinds: "any",
                onSelect: function(file) { 
                    // do something fun with the file object
                    myCoolFunction(file[0]);
                }
            });
            
            e.preventDefault();
            sheet.show();
        });';

        $this->EE->cp->add_to_foot('<script type="text/javascript">'. $script .'</script>');
    }
}
else
{
    $this->EE->load->library('filemanager');
    $this->EE->load->library('file_field');

    foreach( $fields as $k => $field)
    {
        $config = array(
            'trigger' => '#thumbnail_trigger_'. $k,
            'field_name' => '"#thumbnail_'. $k .'"',
            'settings' => '{content_type: "img", directory: "all"}',
            'callback' => 'function(file, e) { 
                // do something fun with the file object
                myCoolFunction(file[0]);
            }'
        );

        // Pass the config to the file_field, it is responsible for loading all JS assets.
        $this->EE->file_field->browser($config);
    }
}

helper.js

Publisher.assets_choose_file = function(button, event)
{
    var $container = button.closest(".file_field");
    var $file_set = $container.find('.file_set');
    var $input = $file_set.prev('input[type=hidden]');

    var kind = "any"; //field.data("content-type");
    var dirs = "all"; //field.data("directory");

    var upload_prefs = $.parseJSON(EE.publisher.upload_prefs);

    var sheet = new Assets.Sheet({
        filedirs: dirs,
        kinds: kind,
        onSelect: function(file) 
        { 
            var file = file[0];
            var file_parts = file.url.split('/');

            var file_name = file_parts.slice(-1)[0];
            var thumb_url = file.url.replace(file_name, '_thumbs/'+ file_name);

            for(dir_id in upload_prefs)
            {
                path = upload_prefs[dir_id];
                if(file.url.indexOf(path.url) !== -1)
                {
                    var directory = dir_id;
                    var file_path = file.url.replace(path.url, '{filedir_'+ dir_id +'}');
                    break;
                }
            }
                
            $file_set.removeClass("js_hide").find('.filename').append('<img src="'+ thumb_url +'" /><br />'+file_name);
            $file_set.next('.no_file').addClass('js_hide');

            $input.val(file_path);

            $file_set.find('.remove_file').click(function(){
                Publisher.assets_remove_file(button, event);
            });
        }
    });
    
    event.preventDefault();
    sheet.show();
}

Publisher.assets_remove_file = function(button, event)
{
    var $container = button.closest(".file_field");
    var $file_set = $container.find('.file_set');
    var $input = $file_set.prev('input[type=hidden]');

    $input.val('');
    $file_set.addClass("js_hide").find('.filename').html('');
    $file_set.next('.no_file').removeClass('js_hide');

    event.preventDefault();
}

helper.php

<?php

// Here is a more specific example used in the Publisher module

public function load_file_manager()
{
    if ( array_key_exists('assets', ee()->addons->get_installed()) )
    {
        // Load Assets' assets
        if ( ! isset(ee()->session->cache['assets']['included_sheet_resources']))
        {
            if (! class_exists('Assets_helper'))
            {
                require PATH_THIRD.'assets/helper.php';
            }

            $assets_helper = new Assets_helper;
            $assets_helper->include_sheet_resources();
        }

        $script = '$(".templateTable").delegate(".choose_file", "click", $.proxy(function(e){
            Publisher.assets_choose_file($(e.target), e);
        }, this));

        $(".templateTable").delegate(".remove_file", "click", $.proxy(function(e){
            Publisher.assets_remove_file($(e.target), e);
        }, this));';

        ee()->cp->add_to_foot('<script type="text/javascript">'. $script .'</script>');
    }
    else
    {
        ee()->load->library('filemanager');
        ee()->load->library('file_field');

        // Pass the config to the file_field, it is responsible for loading all JS assets.
        ee()->file_field->browser();

        ee()->cp->add_js_script(array(
            'file' => array('cp/publish')
        ));

        $date_fmt = (ee()->session->userdata('time_format') != '') 
                    ? ee()->session->userdata('time_format') 
                    : ee()->config->item('time_format');

        $this->_setup_file_list();

        ee()->javascript->set_global(array(
            'date.format'                       => $date_fmt,
            'upload_directories'                => $this->_file_manager['file_list'],

            // Set a few vars to empty, otherwise the JS throws errors. We don't need valid values here.
            'publish.markitup.fields'           => '',
            'user.can_edit_html_buttons'        => '',
            'publish.lang.edit_cateogry'        => ''
        ));
    }
}

/**
 * Setup File List Actions
 * 
 * @return  void
 */
private function _setup_file_list()
{
    ee()->load->model('file_upload_preferences_model');
    
    $upload_directories = ee()->file_upload_preferences_model->get_file_upload_preferences(ee()->session->userdata('group_id'));

    $this->_file_manager = array(
        'file_list'                     => array(),
        'upload_directories'            => array(),
    );

    $fm_opts = array(
        'id', 'name', 'url', 'pre_format', 'post_format', 
        'file_pre_format', 'file_post_format', 'properties', 
        'file_properties'
    );

    foreach($upload_directories as $id => $data)
    {
        $this->_file_manager['upload_directories'][$id] = $data['name'];

        foreach($fm_opts as $prop)
        {
            $this->_file_manager['file_list'][$id][$prop] = $data[$prop];
        }
    }
}

Worth noting that, as per the above, the field_name parameter needs to be a jQuery selector for the field to populate, not just the field name like the documentation suggests.