I am assuming that the entire logo with the black background is done on a single pixel layer. If that is the case, there is no quick way of eliminating the black background. That said, if the logo is not too intricate, a nice selection can easily be made and other background colors can be shown. My approach would be:
1. To make the background a layer, double click on the layer icon and Photoshop will suggest the layer name Layer 0. I suggest you name it "Logo"
2. Using the quick selection tool, select the black background. Then press Shift-Ctrl-I to invert the selection
3. Click on the white disk at the bottom of the Layers palette to add a layer mask. This will eliminate the background
4. If you are using CS5, you are in luck, click on the layer mask and then "Mask/Mask edge" and refine the edge using the smart radius.
You may need to experiment with the parameters, but this will give you a nice clean image against any background you may place below it. If you are not using CS5, you may need to play with the mask layer using Gausssian blur to soften the edges, or before you add the layer mask, feather the selection by a few pixels depending on the image size.
The moral of the story, do not create the background on the same layer as your image if different colored backgrounds are a possibility.
