Because templates are just normal pages with a specific type of content on them, there is no one set-in-stone way of finding a list of templates. However, the majority of MediaWiki sites will use a Template namespace for keeping templates together and easily implementable.
To get a list of all pages within a given namespace, go to Special:AllPages; at the ...
Square brackets instead of braces.
<noinclude>This is a template to mark articles that needs an update. All these articles are listed under [[:Category:Articles that needs update]]</noinclude>
<includeonly>[[Category:Articles that needs update]]</includeonly>