How to connect thermostat to newly-installed condenser/evaporator unit
In the condensing unit, locate the contactor. There should be at least two low voltage terminals on the contactor (commonly on the side). Run a two wire cable between the condensing unit, and the furnace. Connect the wires from the cable, to the low voltage terminals on the contactor. In the furnace, connect one of the wires from this cable to the Y terminal, and the other to the C terminal.

At the thermostat, connect the yellow wire (or any additional wire in the thermostat cable), to the Y terminal. Connect the other end of the yellow wire (the wire you connected to the Y terminal of the thermostat), to the Y terminal of the furnace.

Notes:


These are general instructions, as you have not listed the make and model of the equipment you're using.
You may have to adjust the blower fan speed when in cooling mode.