How to take an image with a white background and make it transparent

Bitmaps (i.e. files with .BMP extension) do not natively support transparency: you need to save as a different format like PNG. Another format that supports transparency is GIF but it is only suitable for simple images with few colours. The best format depends on the image and where it will be used.

If the background is transparent then in Photoshop and most other image editors you would normally see a checkered background made up of small white and grey squares. But the Windows Picture Viewer itself is no good for testing transparency - it shows transparent areas as being white.

Update

Since this answer was originally written (some 8 years ago) it has been pointed out that the BMP format can support transparency in some cases. Still I would not recommend using it for this purpose, many programs will not interpret the alpha channel correctly and there would be no real reason for using it over something like PNG.

you could probably magic wand the white background, and delete it, or create a new layer, and hid the background before saving it.