These tips are probably in the links given above, but some of them may be difficult to find (and the exact syntax may be a moving target):
You can use algebra as follows:
(Scotland OR "United Kingdom") "crime statistics"
"OR" must be all caps.
"+" can be used to include "stop words" that would otherwise be ignored.
It can also be used to make Google look up the exact word (no synonyms, inflection, etc.), e.g.
+book
is not the same as
book
Google can be used to do conversions:
5 USD in EUR
50 mph in km/h
50 km/h in (attoparsecs per fortnight)
You can look up definitions:
define:metonym
Remember to click on the link to the English definitions, if that's what you want.
You can combine various syntax elements:
(+organize OR +organization) (site:ac.uk OR site:gov.uk)
And the example for missing words in the Google Help is not very useful:
Kolumbus entdeckte *
A better example for a translator or someone learning English might be:
"was a very * performance" -"good performance"
Also, don't forget other Google products,like Google books.
And Google labs have some products that haven't quite made it yet, like
http://labs.google.com/sets For instance, if you can't quite remember a figure of speech, type in "simile", "metaphor", "allusion" and see what Google finds.