The outer plastic housing just clips on but tends to break when you pull it apart, not an issue if you're replacing it at the same time replace the "rubber buttons" these are also cheap and makes the whole lot as new genuine covers start at about £15
Courtesy of Andy Monty - this is the top hit on Google using 'dismantling Fiat keyfob'
I looked this up within one hour of getting my new 500 home! My ONLY fob is in a shocking state, would like to get it fixed before I head over to Fiat to spend 100££££££s on new replacement keys
Please let everyone know if it is helpful to you, thankyou