How to change the Battery
How to replae the Battery in Mac Book Air 13 inch?
1.8GHz dual-core Intel Core i5 (Turbo Boost up to 2.8GHz) with 3MB shared L3 cache
You will need to firstly take out all the external screws holding the back case on and then the ones around the battery holding it in (screws can be different sizes so make sure you remember where they go), carefully remove the ribbon connector at one side, then lift out the old battery with the tabs and replace with the new one plugging the ribbon back in and clicking into place then just return all the screws to their holes and replace the back case.
I think videos show this sort of thing best so I've included links below;