Every character has their own special moves with different inputs, they are not all listed, because listing them all would lead to quite the long control list.
The original Mugen way would be to go into the character files and look into the command file. Though I can see that that would be difficult with the web version. As far as I know the original Mugen did not have any way to look at the commands in-game, might be worth adding something like that to Dolmexica especially for something like the web version.
In a more practical way, a lot of characters have moves that are based on quarter-circle motions of the analog stick/dpad/arrow keys, you can get most of the characters to use special moves with that.