How to upgrade Macbook Air 2014 SSD?
In some Macbook Airs the SSD is actually replaceable. Please refer to iFixit.com and the other answers for details. 

However, a very interesting option is to make use of the SD card slot. There are a number of products out there that will fit seamlessly into your SD card reader slot. You can then mount it as an additional drive and put e.g. your music library onto it. Some examples (feel free to update):


Transcend Jetdrive Lite
PNY StorEDGE
Nifty MiniDrive
Sandisk miniDrive


Using one of these solutions you could add up to 256 GB (2015) of storage to your Mac.