There are 4 vase pieces in Winhill, and it is up to you to find them. Talk to the guy standing on the stairs in the mansion to start the quest.
1.) The first vase piece is in the flowers inside the house with all the flowers in it and the old lady.
2.) The second vase piece can be obtained by hitting the tiny chocobo until you get it in the chocobo crossing.
3.) The third can be obtained by talking to the woman in the house that used to be Raine's, twice. Then, go down to the first floor to see a ghost of Raine!!!! Talk to the cat and it'll leave the vase piece.
4.) The final vase piece is harder to get. You cannot have re-named any characters (meaning, if you named Squall "Paul", forget getting the piece). Talk to the medieval armor standing in the mansion and it will give you to last piece. Take them to the man who gave you the quest.