To get the menu:

$menu = JFactory::getApplication()->getMenu();

To get menu items by attribute:

$items = $menu->getItems('menutype', 'mainmenu');

The variable $items is an array of menu item objects. It contains the following:

• id
• menutype
• title
• alias
• note
• route
• link
• type
• level
• language
• browserNav
• access
• params:protected
• home
• img
• template_style_id
• component_id
• parent_id
• component
• tree (Array)
• query (Array)

To get the active menu, and then its parameters:

$current = $menu->getActive();
$params = $current->params;
$yourParameter = $params->get('yourParameter');

To get the default item by language code:

$default = $menu->getDefault();