3. Activate the Elliptical Marquee tool, and on the tool's option bar set the feather to 25 (experiment with this value as it determines the vignette effect) . Drag out the ellipse to embrace what you wish to retain
4. On the blank layer with the oval, fill the oval with Black (Edit>Fill Selection>Foreground color)
5. Copy the Background Layer and place the Background Copy Layer above Layer 1, then group these layers (Press CTRL+G)
6. Shut off the visibility of the background layer.
7. You will have the vignette surrounded by transparency. You can place a background behind this - any color, a gradient, a texture, etc.
Although it is not shown in Jeff's download of the image which has a transparent background, I think you are trying to achieve a vignette effect with a white or lightening effect rather than the usual darkening of the edges. You can create this effect easily in the Vignette Effect found in the Guided Edit>Basics tab. In my screenshot below, I am also showing the layers in Expert Mode, created by the Guided Edit.
And here is a YouTube tutorial I created to demonstrate how to create a vignette effect with any color. If you really want to have an image fade into a transparency, let us know and we can explain how to do that too.