How to make older iPhone and iPad with < iOS 8 enter two factor verification code?
This stumped me for several attempts, until I carefully re-read the pop-up window with the verification code (I didn't take a screenshot, I'm going from memory):

enter the verification code after the password INTO THE PASSWORD field (my CAPS)

So, there is no separate box or window for the verification code. You have to type both the password and code into the same box as one long string.

This worked for me in iOS 5.1

Looks like a way to retro-fit 2-factor into iOS5 without having to release an update.