The way to fight Akuma is the same as it was in the original game. You must not continue, and you must defeat all opponents before M. Bison within 20 minutes or less. When you fight Bison, Akuma will appear, perform the Shun Goku Satsu on Bison, and fight you.
For all classic modes, selecting Akuma is the same as selecting him in the original version. You must highlight these characters for at least 2 seconds in the following order: Ryu, T. Hawk, Guile, Cammy, and Ryu again. Then, after highlighting Ryu for 2 seconds, press Start and all three punch buttons in quick succession. If you did it correctly, Akuma's portrait will replace Ryu's.
If you entered the code correctly, you will hear a sound. The classic versions do not have super combos and cannot reduce throw damage.