You can enable anonymous users (sometimes also called unauthenticated users) to search public pages of your portal by using a portal search portlet.
To do this, make the Search and Browse portlet or the Search Center portlet available on a public page of your portal, so that users can access them without having to log in to the portal.
You also need to enable public sessions for your portal. The reason is that both the Search and Browse portlet and the Search Center portlet need a valid session for their run time, and by default, sessions are not enabled on anonymous pages in the portal. By default, sessions are only created when a user authenticates and logs in to the portal.
Take a look at Infocenter document for step by step procedures on how to enable search for anonymous users