http://www.ifixit.com/Guide/MacBook+Air+13-Inch+Mid+2011+Battery+Replacement/6359
One of the reviews from the amazon link below state that you may need to delete the system preference file /System/Library/Extensions/IOPlatformPluginFamily.kext/Contents/PlugIns/ACPI_SMC_PlatformPlugin.kext/Contents/Resources/MacBookAir4_2.plist to get the CPU throttling working normally.
My Mac
1.7 or 1.8 GHz (Mid 2011) 13″ MacBook Airs
My Battery Specs
Power Rating: 6700 mAh
Model #: A1405
http://stores.ebay.com/toppowerusa/
I ended up buying from the seller on ebay. The Battery had 8 cycles on it and was in close to new condition. It also shipped with the pentalobe screwdrivers (2 of them) required to unscrew the macbook air and remove the battery.
current max: 6778 mAh
original max: 6700 mAh
health:101%.
cycles: 8
manufacture date: 7/24/12
Installation was very quick and easy, just unscrew and replace.