NodeBB comes with a built-in search plugin known as DB Search. This is a simple full text search that will work well for most forums.
If your forum has existing posts, you'll want to make sure these are indexed for search. After restart, select Plugins > DB Search, and hit the Reindex button. You should only need to do this once, since any new posts will automatically be added to the index.
Note that a direct link to the advanced search can be added to your forum by going to the General > Navigation menu in admin. From here, you can select options for this link, including limiting it to only certain users.