Proper use of const regarding member functions

When defining a member function one can use the const keyword in a nubmer of places. I would like to check on the subtleties of location.

If my method merely returns an integer (say a counter) then I could define it thus:

int GetCounter() {return fCounter;}

If I want to ensure that the function does no change the member variables in any way I can add const

int GetCounter() const {return fCounter;}

What I would like to find out about is what it means exactly to use the const keyword in the following three cases:

int GetCounter() const;
const int GetCounter() {return fCounter;}
const int GetCounter() const {return fCounter;}

Thanks