How is the Air Conditioning wiring supposed to connect to my furnace?
Wire colors with HVAC wiring are non-standardized, so the colors themselves don't help much.

Your furance/air handler should have a control board with terminals labelled R, W, Y, G and C. There should be an existing wire that connects to all of these (though maybe not C) that goes to your thermostat. 

If anything is different in your setup, please update your question with a picture explaining, don't just wire it as I described or you may damage something.

The A/C unit wires connects to Y and C (usually white on C, but it doesn't really matter). 

For reference:


R = power (24VAC)
Y = cooling
W = heating
G = fan
C = common power (24VAC with R)




Since this happens a lot, I'd also highly recommend putting some mechanical protection on this wire. Since it's already disconnected, it should be easy to fish through now.

Some flexible ENT tubing might be the easiest option:



1/2" rigid PVC conduit could also work, you can get elbows and other connectors. 

 

All of this should be available at your local electrical / big-box hardware store.