UMN Search: Viewing Google Analytics Search Reports
If you are using the Google Search Appliance and have your Google Analytics account configured (as outlined in the Configure Unit Branding and Navigation for Search Results article), then you can access the search reports in Google Analytics. The search reports will give you useful information about what visitors are searching for from within your site.
The reports are fairly self explanatory, giving information about what visitors are searching for, where they're searching and percentage of visitors using search. For more information about the reports, please refer to the Google Analytics Help Center