Air Conditioning - Step by step A/C troubleshooting?

Dear experts,

Could you please get me started with a step by step troubleshooting of my central A/C?

Here is the problem... I bought this place in December and never bothered to check A/C until now. :wall: Well, the A/C does not work at all. The furnace blows warm air and the A/C unit never kicks in. I have reasons to believe that the problem might be with wrong wiring (in early spring I replaced a thermostat and fished a new thermostat wire so there is a chance I messed something up along the way).

Starting with the thermostat or the furnace what voltage should I check for? Across what terminals? What should I check next?

Here is my thermostat wire connections inside the furnace:
24V (Red) to R
Fan (Green) to G
Heat (White) to W
AC (Yellow) to Y
Common (Blue) to C.

EDITED: After posting the message I found out that there is a 2 wire (white and red) electrical cable that goes from the A/C outside into the furnace control panel. However, it is not attached to anything. I am pretty sure this is exactly why the A/C is not working. What should I connect these wires to???

Thank you!

Bbyaka

One of them goes to Y, the other to C.