How can I tell PyCharm what type a parameter is expected to be?

Yes, you can use special documentation format for methods and their parameters so that PyCharm can know the type. Recent PyCharm version supports most common doc formats.

For example, PyCharm extracts types from @param style comments.

See also reStructuredText and docstring conventions (PEP 257).

Another option is Python 3 annotations.

Please refer to the PyCharm documentation section for more details and samples.

PyCharm extracts types from a @type pydoc string. See PyCharm docs here and here, and Epydoc docs. It's in the 'legacy' section of PyCharm, perhaps it lacks some functionality.

class King:
    def repress(self, peasant):
        """
        Exploit the workers by hanging on to outdated imperialist dogma which
        perpetuates the economic and social differences in our society.

        @type peasant: Person
        @param peasant: Person to repress.
        """
        peasant.knock_over()   # Shows a warning. And there was much rejoicing.

The relevant part is the @type peasant: Person line of the docstring.

My intention is not to steal points from CrazyCoder or the original questioner, by all means give them their points. I just thought the simple answer should be in an 'answer' slot.

If you are using Python 3.0 or later, you can also use annotations on functions and parameters. PyCharm will interpret these as the type the arguments or return values are expected to have:

class King:
    def repress(self, peasant: Person) -> bool:
        peasant.knock_over() # Shows a warning. And there was much rejoicing.

        return peasant.badly_hurt() # Lets say, its not known from here that this method will always return a bool

Sometimes this is useful for non-public methods, that do not need a docstring. As an added benefit, those annotations can be accessed by code:

>>> King.repress.__annotations__
{'peasant': <class '__main__.Person'>, 'return': <class 'bool'>}

Update: As of PEP 484, which has been accepted for Python 3.5, it is also the official convention to specify argument and return types using annotations.

I'm using PyCharm Professional 2016.1 writing py2.6-2.7 code, and I found that using reStructuredText I can express types in a more succint way:

class Replicant(object):
    pass


class Hunter(object):
    def retire(self, replicant):
        """ Retire the rogue or non-functional replicant.
        :param Replicant replicant: the replicant to retire.
        """
        replicant.knock_over()  # Shows a warning.

See: https://www.jetbrains.com/help/pycharm/2016.1/type-hinting-in-pycharm.html#legacy