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According to some reports, the page has been redesigned and it now hides some of the obscure features inside a plusbox, while offering tips and a preview of the query:
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The update is still being tested and it's likely you don't see it yet at: google.com/advanced_search.
For the time being, I suggest to use the advanced search for the option hidden in the expandable box (date, keyword location), while using the search operators for the other options. Some example of queries that use operators:
* paris -hilton site:edu (all the pages that contain Paris, but not Hilton and are from .edu sites)
* "women's rights" site:en.wikipedia.org (all the pages from Wikipedia that contain the exact text "women's rights")
* shakespeare inurl:hamlet filetype:pdf (all PDF results that contain Shakespeare and have Hamlet in the URL)
For the average user, the new page is more approachable, but Google's challenge is to provide good results even if you don't refine the query using operators and advanced operators.
{ The second screenshot has been licensed as Creative Commons by Barry Schwartz. }