The main way to handle monads is do-notation. It can "unwrap" monads easily, with do and arrows. Here is an example with the IO monad, inside of the main function.
main = do
fileHandle <- openFile "test.txt" ReadMode
x <- hGetContents fileHandle
let x-lines = lines x
In this block of code, the Handle is "extracted" from the IO Monad in the second line of code. <- will take a Monad, and bind its wrapped value to a named value. Note that this is still lazily evaluated. Afterwards, a new String is taken from an IO (String) and put into x. The next important line, "return ()", uses one of monad's core methods. This is because main must return an IO monad. However, you can see that it is inefficient to bind so many variables. So, here is how to use another one of Monad's methods, >>=, to chain actions together.
main = do
xlines <- openFile "test.txt" ReadMode >>= hGetContents
This is such an essential usage of Monads that >>= is the unofficial symbol representing Haskell. As you can see, the result of the openFile command is "pushed" into hGetContents. It's important to note that a monad is going into hGetContents, and a monad is coming out. <- is what unbinds it.
Functors and Monads
So, you still have to use the <- to "de-monad" the monad you get before it can be used, right? Wrong. There is a typeclass called fmap, which is generally applicable to everything. One of the monad laws dictates the behavior of fmap, so it damn well better be able to manipulate our monads. Here is the program once again rewritten:
main = fmap putStrLn $ openFile "test.txt" ReadMode >>= hGetContents
Here, fmap is a function with the type signature of "String -> IO ()", applied to the result of hGetContents on the monad pushed into it by the openFile. fmap maps putStrLn over the results, and the IO is returned as a result. Nifty? Nifty.
So, the last piece of the puzzle is this: You have multiple monads, and you want to add the result of them without binding temporary variables. This can be done with Applicative Functors. They are like Functors, but with some added goodies. To use Applicative functors, include Control.Applicative and test out this chunk of code:
main = fmap putStrLn $ pure (++) <*> (openFile "test.txt" ReadMode >>= hGetContents) <*> (openFile "test2.txt" ReadMode >>= hGetContents)
This will take the ++ function, turn it into one which can work with Applicatives, and then apply it partially over the <*> elements. If the function can already handle Applicatives, then <$> can be used instead.
Monads were a tricky subject for me for a long time. Most of my programs look like my first chunk of code, where I did one monadic operation per line. However, learning to master Monads in Haskell to control side-effects and efficienty keep track of your state is of utmost importance in commanding the language. So go on, don't pick up that monad. Wear that >>= with pride.