Most wrong expectations about site search come from assuming the index holds everything. Start with What the index holds: which record types are indexed, the three conditions a record has to meet, and why area text is invisible until it is mapped. Search fields then shows how to map it, and how one field makes pages, posts and products come back with the same parts.
Search views covers the record that defines each search, and which of its settings a visitor can change from the URL; read it before configuring a view on a live site. The last two pages are for when something is missing: Reindexing lists what updates the index on its own and what leaves it stale, and Why a new record is not findable yet is the diagnosis, step by step.