Edited 5/16/19. This was a beginner question, and I worded it all wrong because there was so much stuff I didn't understand.
My understanding now is that before creating an animation I need to create all the objects I expect to need in the 3-D View panel. I can't add a new object once there are lots of keyframes and tweening happening, because the existing keyframes may interfere with the new object. There are also mysterious things called "actions" using advanced editors that I know I will never understand.
When I create a Material with .5 alpha, I cannot assign it to the selected object.
I'm looking for a solution that tweens the alpha property of an object, so that an object gains or loses visibility gradually. If this really cannot be done in Blender, please someone post "this cannot be done in Blender". I would be surprised, since Blender can do everything else.
I apologize for being such a beginner. I started learning using cgcookie.com, but after the success of the first course I couldn't keep up with the fast videos and had to quit. I now search the web to learn each new thing I need in Blender, so this question of animating the alpha channel is probably useful for others, too.