I’m amazed by everyone else’s MUCH more complicated answers.
XML
You can very simply define the alpha in the color definition of the button (or any other view) in your xml:
android:color="#66FF0000" // Partially transparent red
In the above example, the color would be a partially transparent red.
When defining the color of a view, the format can be either #RRGGBB or #AARRGGBB, where AA is the hex alpha value. FF would be fully opaque and 00 would be full transparent.
Dynamically
If you need to dynamically alter the opacity in your code, use
myButton.getBackground().setAlpha(128); // 50% transparent
Where the INT ranges from 0 (fully transparent) to 255 (fully opaque).