All words (default):

cats dogs

Any of these words (OR):

cats | dogs

One word but NOT another:

cats -dogs

Exact phrase:

"i like cats"

Proximity, when words occur within 5 words of each other:

"cats dogs"~5

Order, when words occur in a particular order:

cats << dogs

The start of posts:

^cats
"^I like cats"

The end of posts:

cats$
"I like cats$"

Posts that contain nothing else:

^cats$
"^i like cats$"

Combinations:

(cats | dogs) squirrels
(cats | dogs) -squirrels
(cats | dogs) (squirrels | llamas)