Summarize:

To turn off the background layer of your image, click icon that resembles an eyeball at the next to the background layer in the Layers panel to the right. This disables the background layer and removes the background. You now have an object with a transparent background that can be overlaid onto any other existing image. You'll need to save the iamge in an image format that supports transparent images. Use the following steps to save your image: Click File Click Save as. Enter a name for the file next to File Name. Select PNG, GIF, or PSD in drop-down menu next to "Format." Click Save
Turn of the background layer. Save your image.