Margo, What you have is called the TIP TOE WASTE. Several manufacturers make it.
If you have trouble getting it together you maybe better off taking it to a local plumbing supply and showing them the parts in your dainty hands.
This way they can atleast give you the proper thread connection in case the rubber disc part is no longer plyable to stop the water.
If it can be put back together they should be able to do that also
Have a great week end
SylvanLMP