Thousands of people have tried to play Minecraft Classic, but can't since Java 7 doesn't work right. First follow this article/tutorial on how to switch internet java back to Java 6 in order to play Classic.http://support.apple.com/kb/HT5559??
Now make sure to follow this article exactly or it might mess you up.
After you have completed this, go to http://minecraft.net/classic
then chose the mode you want to play on (singleplayer or multiplayer). After you do that you will most likely see a black square on the screen with the java logo on it. Some messages will start asking permission to use java for minecraft. Instead of clicking anything yet, reload the page while holding command+shift. Don't let go of command+shift, now move your mouse over the black box. A white windowed edge will appear with the normal red exit button and such. Drag the window with your mouse. Once the window is moved a bit, let go of command+shift. The same permission messages will start displaying, press "Always allow" for each on until they stop appearing. If everything worked, then you should have a playable Minecraft Classic. Enjoy.
I'll make a video tutorial if there is a lot confusion about how to do this. For other simple things just ask here. Also, if it works for you tell me so I can know if my information is accurate. Thanks.