The basic search is a Boolean search. You can type in keywords that you're looking for in a document and use NOT to keep out what you're not looking for. For example, whenever I search for 'Georgia' I always add 'NOT constitution,' otherwise I'd get thousands of results back from newspapers.
The Beta search is pretty good. It's an advanced sort of search, where you can search for keywords inside of an already exhisting search. For example, after searching for 'Georgia NOT constitution,' I can then search for 'Emanuel county.'
What's difficult is that not all documents have good keywords attached. It's nice when users have added annotations to documents, which is like adding searchable keywords. This will be what makes this site great - interactions from users.