One way to do it would be to go to the layer drop down menu and select- layer from background. after you do that,go to the opacity slider in the layer palette and fade it to whatever you want.
Before you do that, make sure the Background is turned into a Layer by double-clicking on it (or Alt double-clicking to avoid the naming dialog).
FYI: Edit>Fade is used not to fade a picture, but to back off from the effects of a filter or adjustment. For instance, try running Levels on an image and then go to Edit>Fade to knock back the effect by some percentage.
When I did those steps I get a grey/white checkered background and the only way I got rid of it was to flatten the image.
the checkered background indicates transparency. when you save in a format that supports transparency (gif or png for example) you can then use that image on a web page (or page layout app, etc). the places where you see the checkerboard in photoshop will be see through (transparent) on the web page.
You can set the background in your prefs to be the checkered,or not at all if you want it that way.