Before you do anything else with the computer, clean the motherboard to keep it from getting worse. Remove the motherboard and clean every spot you see that is questionable. If it's extreme, you may have to use an ultrasonic cleaner to do it. You will also want to replace the battery, especially for the MBA. This is a soft cell pack, making it a major risk compared to a plastic encased pack. Being internal certainly doesn't help.
Outside of the battery, you will probably need a new keyboard. These are very commonly destroyed with liquid damage. I wouldn't bother trying to recover any corroded cables. You're better off replacing them and being done with it one time.
Now that you know what you need to focus on with this machine with the liquid spill cleanup and what to replace, now you need to know what to get to do it. For starters, either a antistatic brush, a toothbrush or a ultrasonic cleaner. The downside to the brush method is you can't clean under any chips, so there will always be corrosion. Because of this, I no longer recommend this if anything got next to a BGA chipset and you will have to replace any damaged chipsets if this is the case. At this point, jump to the ultrasonic cleaner and clean it that way to make sure. However, alcohol and a toothbrush may be fine if it's nowhere near any BGA chipsets.
You are going to want to use 99% Isopropyl alcohol. This is because rubbing alcohol can damage motherboards. The guides you need to open the machine with are below. You will not find one for the keyboard, so you need to source that out yourself, and potentially other guides. You are also going to need thermal paste to replace the existing thermal paste. You can get this from places like Amazon, or Radio Shack stores that still sell it. iFixit sells it too. For the tools, you will need the following:
MacBook Air 13" Mid 2011 Logic Board Replacement
MacBook Air 13" Mid 2011 I/O Board Replacement
Once you finish cleaning the board, reset the SMC and PRAM. This is more or less so the SMC is clear from any junk from before and is merely to make sure. Since the MBA is a "sealed" machine, it doesn't reset the same as the machines with replaceable batteries. I have posted the procedure below, per Apple's website. You can see the instructions on a SMC reset below. Considering the board is clean, this will give you a way to troubleshoot at the board level where you know nothing is screwy where it shouldn't be.
Shut down the computer.
Plug in the MagSafe power adapter to a power source, connecting it to the Mac if its not already connected.
On the built-in keyboard, press the (left side) Shift-Control-Option keys and the power button at the same time.
Release all the keys and the power button at the same time.
Press the power button to turn on the computer.
Note: The LED on the MagSafe power adapter may change states or temporarily turn off when you reset the SMC.
Now, reset the PRAM.
Press Command, Option, P+R at the same time before it boots. The machine will restart if done correctly.
If you need better instructions on these resets, read this.