I want to know which two wires it connects together to activate the AC
Which two wires? That's all going to depend on the AC system and how it is wired; technically, there is a standard, but anybody who has ever looked at an AC system knows that such "standards" are sometimes not followed at all.
If you are asking this question - you have no business messing around with your AC wiring. But I'll tell you how you would figure it out:
First, if you don't have a thermostat connected (and just a bunch of wires dangling out) - you would first go to your breaker box and shut the power off to the AC unit (alternatively, you can pull the fuse pack or breaker at the AC unit itself). You need to do this because the AC unit uses a transformer to convert the line voltage to a lower voltage (usually 24 volts AC) to operate the relays. This voltage is present on the wires coming into the house, and while it isn't lethal, it can be unpleasant to come into contact with, and you don't want to short anything out, either. So disconnect the power (this is like, rule #1 when working on -any- circuit; if you haven't learned this, you shouldn't be touching an Arduino, let alone your AC unit).
Once the power is off, you would then count how many wires you have (usually, it will be 4 to 6 wires), and note on a sheet of paper the number and color of each wire. Then you take that piece of paper with you back to the AC unit. Make sure you have some tools with you. Also - if you have it - the manual to the AC unit will be helpful; hopefully it has a schematic of the wiring for the unit. Verify that the manual matches your AC unit (you wouldn't believe how many times the manual for an AC unit a homeowner has doesn't match their unit). Compare model numbers and such.
Now - at your AC unit, there should be an access panel. If not, you might have to unscrew and remove more than one panel. Don't lose the screws! Make sure you can put it back together again (depending on the age of the unit, they can be real tricky to take apart and put back together). Something to note is where the control wires (from your house) come into the system; you'll either have a small conduit, or just a thin cable (compared to the line voltage cable - which will usually be about an inch or so in diameter) running into a bottom or side panel. Note where it goes in.
The access panel -should- (once you have it opened up) have inside the controller board, relays, and low-voltage transformer for the system; the control wires should connect (via screw terminals, or via crimp/spade terminals, or similar) to it. Find those wires, then note the color of them (remember your notes?) and what terminal or whatnot they are connected to. If there are letters or numbers next to the terminals, note all of that down. Keep very good track of everything.
Once you know all of that - then you can reference your schematic (if there isn't one in your manual, there is likely to be one on the inside of the panel, or on the back of the removable panel). If despite your best efforts you can't find a schematic, then you might go online and look it up, or contact the manufacturer of your AC unit. You may or may not be able to easily get such a beast (you wouldn't believe how hard they make this - not only can it sometimes be close to impossible to get such information, but buying new parts like relays and contactors can be a real exercise in frustration; I think they do this purposefully to keep people from killing themselves playing around with their AC unit - they aren't exactly safe things if you -don't- know exactly what you are doing).
Anyhow - with the combination of the wiring diagram and colors, and the schematic - you should be able to work out what wire is "common" and what wires that common should be connected to in order to activate which functions. Typically, most AC units will have something like a internal fan function, a compressor function, and a heater function; some will have an "external fan" function as well; heat-pumps typically have things labeled slightly differently, but functionally they are very similar in operation.
Once again - don't play around with this stuff if you don't understand or have an inkling of what you're trying to do. The fact that you asked such a question says to me you aren't ready to tackle such a job - especially if your unit is on your roof (up on a roof, playing around with a line-voltage appliance, even when it is off - is not something you do willy-nilly; a roof is a dangerous place to be on a house, and a ladder is one of the most dangerous tools a homeowner can own, second only to a chainsaw - now just think about those poor saps who use chainsaws on ladders to cut limbs off their trees!).