One way make a background transparent is to delete the Background Layer in a Photoshop image, leaving the layers above it visible. Then save the image as a GIF or PNG.
An alternative and easy way to save a partly transparent image is to do the following.
1. When you’re finished working on your web graphic, choose Save For Web. This opens the Save for Web dialog box.
2. From here, select the eyedropper tool and click on the colour in the image that you want to make transparent.
3. Click on the Colour Table in the bottom of the dialog box and click on the first icon. The colour which you selected is highlighted on the colour table and at the same time that colour becomes transparent on your image.