The controls for the furnace/air handler/AC system operate on 24 volts. One side of the 24 volt transformer connects to the red wire terminal, the other side of the transformer would be the c connection. In the diagram below, the c wire would be the wire from the transformer that connects to the common side of the fan, heat, and A/C condenser relays. I would just cut the c wire, strip the ends and wire nut it to your c wire going to the thermostat. The combination of a c and r wire at the thermostat gives the stat continuous 24 volts, which is what it wants.

Examine where the current thermostat wiring connections (R, G, Y, W, etc.) are connected to the air handler control board. Each terminal has a letter associated with it. See if there is one marked "C". If there is then that is the connection point of the new wire.