Den Danske Ordborg provides phonetics for a few variations of pronunciation:
[mɔˈsgeˀ] [moˈsgeˀ] [ˌmɔsge] [ˌmosge]
The verb 'ske', and Norwegian 'skje', both/are both from Low German (as many borrowings are) schehn (from Old Saxon skehan, from Proto-Germanic skahaną), meaning to happen or occur, or to spring up (related to shake, from Proto-Germanic skakaną).
While Norwegian has 'kanskje', literally 'can-be', Danish has 'måske', literally 'may-be'. This represents the same idea as English 'maybe' or 'mayhap'.
Don't be angry; it's really not hard at all.
On the Macintosh, at least with a standard British, U.S. or Canadian keyboard, it's just "option-a" to get the Nordic A-ring character.
On the PC, you can hold down the ALT key whilst typing 0229 on the numeric keypad.
However, unless you're used to regularly typing these key combinations for entering large amounts of Danish or Norwegian text, the simplest way — for the purposes of learning Danish or Norwegian — is to just use the Duolingo interface.
On the Duolingo dialogue boxes you're already using to answer the little test questions, there are three little buttons below the typing data-entry field. Just click with your mouse on the character that corresponds to the character you want. That way you can easily get an æ, ø or å, as needed.
Have fun with learning Danish. Godaften, Eriko