DotNetNuke provides Search Skin object to provide search input for portal and Google search, there are no other search engines supported.
Besides there is a SearchInput module, which can be used instead of the skin object and placed in any pane on a page.
After submitting a search request, the results are displayed in the SearchResults module. This module has to be installed once and only once on any page of a DNN site - including the recycle bin. It retrieves results from the search index, which is implemented via the SearchStorage Provider. The search store is updated frequently by a scheduler job, which calls all modules (precisely, all modules implementing interface iSearchable) of the site, using the SearchIndexing provider.
The 5.6.0 release includes an enhanced indexing capability which allows the standard core search feature to index page names, tag attributes and other metadata for improved search results.
Note: Search indexing in DNN community edition has limited support for non-Latin characters.
The Professional and Enterprise Editions contain a new Site Search engine which allows site users to quickly locate files and pages in the site. The search engine includes rich query syntax with support for Boolean searches, phrase searches, relevance searches, wild cards, fuzzy searches, and groupings. Based on Lucene, the system includes a true web spider that is capable of indexing any site, whether it is built on DotNetNuke or not.
With the 7.1.0 release, DNN changed search to use a more powerful lucene based search. To read more about it click here
Note: to read about how to integrate with it, click here
A useful presentation on the design can be found here
Using Luke to peek into Lucene Search Database, click here