How to use the priority queue STL for objects?

You need to provide a valid strict weak ordering comparison for the type stored in the queue, Person in this case. The default is to use std::less<T>, which resolves to something equivalent to operator<. This relies on it’s own stored type having one. So if you were to implement

bool operator<(const Person& lhs, const Person& rhs); 

it should work without any further changes. The implementation could be

bool operator<(const Person& lhs, const Person& rhs)
{
  return lhs.age < rhs.age;
}

If the the type does not have a natural “less than” comparison, it would make more sense to provide your own predicate, instead of the default std::less<Person>. For example,

struct LessThanByAge
{
  bool operator()(const Person& lhs, const Person& rhs) const
  {
    return lhs.age < rhs.age;
  }
};

then instantiate the queue like this:

std::priority_queue<Person, std::vector<Person>, LessThanByAge> pq;

Concerning the use of std::greater<Person> as comparator, this would use the equivalent of operator> and have the effect of creating a queue with the priority inverted WRT the default case. It would require the presence of an operator> that can operate on two Person instances.