Step 1: The circuit diagram
The switch (not shown in the diagram) is just two strips of metal pressed together, with a piece of paper in between. As the card is opened, the paper is pulled away and the two contact each other, thus closing the circuit.
A fragment of the code is shown, too. The program takes up 56 locations in memory. The PIC10F200 has 256 such locations available. A melody consisting of 200 notes or so can be fitted in to this chip.
This should be sufficient for a musical greeting card.
Step 2: The chip
For a really small card, the SOT23 package can be used. I have tested this with the small versions of the 10F200 and 10F206.
The figure shows a PIC10F206.