Topic on Manual talk:How to make a MediaWiki skin

Languages can be rendered via the data-portlets object (Manual:SkinMustache.php#DataPortletsObject).

If you need to be able to test this locally on a wiki without languages you can use Extension:MobileFrontendContentProvider or skins.wmflabs.org.

With SkinTemplate:

if ( $this->data['language_urls'] ) {

		echo "<ul>";
		foreach ( $this->data['language_urls'] as $key => $langLink ) {
			echo $this->makeListItem( $key, $langLink );
		}
		echo "</ul>";

	} 

With SkinMustache:

{{#data-portlets.data-languages}}
<ul>{{{html-items}}}</ul>
{{/data-portlets.data-languages}}

How can i show the language links to a skin?

I also need to know the options to customize that as well. For example I may want to show the language list as a drop down menu.

Assuming you are using SkinMustache, the template data is described in Manual:SkinMustache.php#Menus. Let me know if anything can be expanded there.

If you are asking how to configure your local wiki to display languages, that's documented in Manual:Interwiki and out of scope for this page.

I was taking about the language links mentioned here: Manual:Skinning Part 2#Language links