[guide|860|Here is the iFixIt guide I followed].
This guide was very helpful and accurate for our A1304 Air, I have commented/adjusted the guide to give some extra info which I felt was missing, useful for identifying the correct model/revision and related replacement part.
I fitted a RunCore 128GB SSD to our A1304 (Revision B) Air, it was easy enough and works exactly as we hoped! The A1304 (Revision B) model Air has a LIF connector. RunCore have different SSD products for the different Air revisions, it would be easy to order the wrong part, so be sure you you what modle/revision of Air you're working on!
Read the guide in full for, for all the details.