If your object is not polymorphic (and a stack implementation likely isn't), then as per other answers here, what you want is the copy constructor. Please note that there are differences between copy construction and assignment in C++; if you want both behaviors (and the default versions don't fit your needs), you'll have to implement both functions.
If your object is polymorphic, then slicing can be an issue and you might need to jump through some extra hoops to do proper copying. Sometimes people use as virtual method called clone() as a helper for polymorphic copying.
Finally, note that getting copying and assignment right, if you need to replace the default versions, is actually quite difficult. It is usually better to set up your objects (via RAII) in such a way that the default versions of copy/assign do what you want them to do. I highly recommend you look at Meyer's Effective C++, especially at items 10,11,12.