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This step is important, otherwise you may see a thin white line between your objects and any background you cut out objects into. |
- Option 1: Selecting only one of the channels in the alpha. Select one of the channels in the channels palette. Then Ctrl+A to select all, then Ctrl+C to copy.
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Click here to download a Photoshop action that does the same thing as the steps described above. To use it, load it first in Photoshop from the Actions palette. Then open your render and alpha image. Click on the alpha image window so it's the selected document, and run the action (default hotkey assigned to it is F12).
A note on black backgrounds when rendering with Alpha channel
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Comparing two renders - with/without a black background. Both renders would produce the same alpha map and the illumination on the sphere itself is exactly the same. The sphere has been rendered deliberately out of focus to show what happens at the edges of objects (which always fade into the background even when in perfect focus because of the antialiasing applied). 
The first sphere has a background which changes in brightness and the out of focus parts of the sphere mix with this changing background. After using the alpha to cut it out of the background, those areas with changing brightness remain. It is not possible to remove them using either "remove black matte" or "remove white matte".
Because the second sphere is against a perfectly black background, there is a dark border left after cutting with alpha, but it can be perfectly removed using "remove black matte".