Unlike previous fighting games, the demo only comes with a single user profile. To play two player vs. mode on the same computer, you are better off creating at least a second profile (3rd option in the Profile menu), then assign it a new control setting (1st option in the Profile menu).
To select profiles at the character select screen, press C to open the profile window. In this window, for both players, the 1st option selects a profile, and the 2nd option is control setting.