The entire HP-42S character set, and the additional characters defined by Free42 and Plus42, are accessible from the pop-up keyboard. The ones that you can't see immediately in the uppercase, lowercase, 123, and #+= layouts are accessible by long-pressing certain keys. For example, when you press and hold the A key, you will see the options A Ä Å Æ ᴀ.
The layout mostly follows the iOS US English QWERTY layout, with of course a few modifications for characters that are in the calculator's character set but not available on the iOS keyboard.