(wikimedia.org) A typical curve showing section lift coefficient versus angle of attack for a cambered airfoil.
Based on the graph above, do negative angle-of-attack values create lift? How?
The graphic above only shows the positive $C_L$ portion of the complete curve. The line (of course!) continues below the zero $C_L$ line.
Also, the $C_L$ curve for any airfoil, symmetrical or not, must cross the $C_L$ = 0 line at some angle of attack. Whether the airfoil is symmetrical or not simply determines what that zero $C_L$ intersection AOA will be. In fact, for asymmetrical airfoils, it is only a matter of convention as to how to define Angle of Attack. Yes, it is the angle that the Airfoil makes with the relative wind (or the flight path through the air), but how the "Airfoil" is defined can vary. In some cases it is defined as the longest chord line through the airfoil from leading to trailing edge, in some cases it is defined by the bottom of the airfoil, etc.
As to the question "How?", all Aerodynamic forces are generated by the pressure of the air pushing on the surface of the airfoil. At each point on the surface of anything in a fluid, the fluid pushes on the surface, normal (perpendicular) to the surface, with whatever pressure exists at that point. What we call Lift is just an abstraction we create to help visualize and do aerodynamics calculations. It is the component of the sum of all those tiny forces added up (actually, integrated vectorially) which is perpendicular to the flight path of the aircraft. Lift is created because when you incline any airfoil, in any direction, the actual normal pressure at each point on the surface changes*, all over the surface of the airfoil, and the total vector sum of all the forces (on one side versus the other) is no longer balanced.