Interwiki
MediaWiki has an interwiki prefix system that lets you search, or link to, external wiki content. And it doesn't have to be "wiki"; it just has to be structured. So, because we have an entry for 'Google' in our interwiki table, you can link to Google results with Google:"Rail+Trail"+Paths+In+Salisbury+Massachusetts.
And you can search Google directly from the search bar of this wiki: Just enter the "shortcode" (Google), followed by a colon (:), and your search query. This works for ALL interwiki prefixes. So, to search Wikipedia for "roses", just enter 'w:roses' in the search bar.
Templates
Templates are useful for linking other search engines. See Help:External_searches for example. You can create a template that makes it convenient for editors to post links to search or database query results in the wiki.
Application (Internal) Native Search
The default search system for MediaWiki is based on MySQL database technology; and is not the most powerful search engine. To make it better, use the Elasticsearch system instead.
Foundation Project
The Wikimedia Foundation has a team called Wikimedia Discovery devoted to search technology.
As of Feb. 2016, it was revealed that the Wikimedia Foundation is working on a grant-funded project to improve Elasticsearch with additional sources of free data and knowledge on the Internet. See Wikimedia Discovery/FAQ