It would be most simple to accept string instead of number (so that you don't have to figure out yourself), but I'm not sure if your tutor will like that.
To extract digits out of a number x, use operators / and %. x%10 is the last digit, x/10 is the whole number except the last. I'll leave the whole algorithm for you to figure out.
Either way you do it, you'll need to define const char* digit[] = {"zero", "one", "two", ...
Instead of cout << some_digit, write cout << digit[some_digit]. The rest is just as hard as printing a number in decimal.
first digit = x1%10
x2 = x1/10
second digit = x2%10
x3 = x2/10
...
until x becomes 0.
You can do it in a loop, or, even better, in a recursive function.