Be straight up and professional in your first request. Make this by whatever communication channel is standard. I would assume e-mail, but someplaces it might be written. Either way it needs to be something you can record and look back to.
Dear Manager
I have been working night shift for 6 months now and would like to respectfully request a shift change to mornings(days whatever you call it).
If you get rebuffed, then you can politely bring up that you were promised 3 months and it's starting to affect your health and you would like a change.
You did not indicate what the need for night shift is and who if anyone would take over. This may be a factor in shifting you or not.
