The thick red wire is the positive power-in, the thin red wire is the positive supply-in for the controller, and the black wire is the common negative. These wires should connect ur battery. If ur battery just have 2 wires, ur can connect the thick and thin red wires together. Be careful, if the negative and the postive are changed, the controller would be burn.
U must make sure ur controller's brake sign. Commonly, 48v controller is "negative". It means if u "brake", the sign connect to the negative. So u can connect one brake wire to the negative, one wire connect to the controller.