Accessing a user's search history
CiviCRM does not store information of who accessed what, for better and worse.

If you have the advanced logging turned on, you can see changes users made.  The CMS may have a record of when they last accessed the site, if that's helpful.  There's also an extension that adds a permission to restrict exports.  While any of those might be helpful, none are what you're looking for, because it doesn't exist - sorry!