+word The word must be contained.
-word The word may not appear.
~word The word should not appear in the record.
Thus ~word is suited to eliminate "noise words".
>word Gives the word a greater standing.
word* Searches for words that begin with word (e.g., word, words, wordless).
"word1 word2" This exact word order should be searched. Case-insensitive.
() Used to group expressions.
A Boolean full-text search might look like this:
SELECT * FROM tablename
WHERE MATCH(column1, column2)
AGAINST('+word1 +word2 -word3' IN BOOLEAN MODE)