Basics:
1) use "+" to include small words, e.g. +the piano
2) A (B or C)
3) * - wildcards for full-word
Short cuts:
4) define xx; or define:xx (the latter returns only definitions)
5) calculator
Syntax:
6) inurl:"x y"
7) intitle:x
8) intext
9) inanchor
10) site
11) cache
12) filetype
13) ~X (synonyms of X)
The book is comprehensive up to its date about Google basics. The search part is not as useful as Google Hacks as the latter provides useful searching tips along Google syntax explanations.