The Erlang way would be to code for the happy path, and not try to anticipate most errors. If your process encounters an error, it will crash, the supervisor will restart it, and it will continue processing. Of course, you can choose to handle anticipated errors if you would like to be more user friendly (e.g. provide a user-friendly message if a file is missing), or if you want to log the error or something. But generally it's considered defensive programming and an antipattern to try and handle every error condition in an Erlang program like you have to do with e.g. Java exceptions.
In languages with powerful type systems like Haskell, errors can be handled by using (for example) the Either[1] type. That way, you are forced to pattern match on the type (it will be a Right if successful or a Left if unsuccessful/errored), so it's not possible to "forget" to check for a null reference like you do in Go (i.e. checking err != nil all over the place).
[1]: http://hackage.haskell.org/package/category-extras-0.53.4/do...