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.
is not the same as
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:
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.