The Monad class is defined like this:
class Monad m where (>>=) :: m a -> (a -> m b) -> m b (>>) :: m a -> m b -> m b return :: a -> m a fail :: String -> m a
All instances of Monad should obey:
return a >>= k = k a m >>= return = m m >>= (\x -> k x >>= h) = (m >>= k) >>= h
Any Monad can be made a Functor by defining
fmap ab ma = ma >>= (return . ab)
However, the Functor class is not a superclass of the Monad class. See Functor hierarchy proposal.
Monads are known for being deeply confusing to lots of people, so there are plenty of tutorials specifically related to monads. Each takes a different approach to Monads, and hopefully everyone will find something useful.