Next use the lasso tool to cutout the inside parts of the image. You do this by holding [Alt/Option] and click with the lasso, then continue until you have covered the part you want to cutout. For this image you will need to cutout 2 places — the hole for the top ring and the hole for the bottom ring.
Next go to [Select->Modify->Smooth] and enter in a radius of 2 pixels. The radius is how much to smooth the selection. If the selection you made earlier is very jagged you might want to experiment with higher radius levels to smooth out the selection.
Next go to [Select->Feather] and enter in a radius of 1. This will blur the edges of the selection a bit and give it a more real look.
Next go to [Select->Modify->Contract] and enter in an amount of one pixel. This makes the selection a little tighter which also helps in making a nice cutout.
After you have done these steps, just copy and paste the part of the image you have now cutout.