A few times my macbook air shut down unexpectedly, with around 15% charge left. I began to suspect battery issues-- and sure enough later that week the machine was telling me to service my battery. As I'd purchased the tools to open it for a previous repair I took of the back plate and saw one of the cells was starting to swell. Replacement time indeed.
The repair was really quite simple. On my phone I double checked the guides listed on the site to make sure I wouldn't put the wrong screws in the wrong places when I was done. Off come the ones for the bottom of the macbook, which comes right off without them. Disconnect the battery, unscrew the screws holding it in. Remove it, replace with the new one, and walk through the previous steps backwards.
With the correct screwdriver this is probably the easiest repair I could imagine doing to a macbook air. It's literally the firs thing inside when you open the case. Don't be worried, double check the guide on the site if you need to. Assuming you have the standard amounts of fingers and thumbs at your disposal you've got this.