e, i, o, and u, are short vowels--they sound similar to the English bet, bit, got, and put, respectively.
ee, ii, oo, and uu are long vowels--they sound similar to the English, bat, beet, fought, and dude respectively.
eee, iii, ooo, and uuu are extra long vowels. They usually have extra stress in the end or the beginning. They are like putting the long vowel oo followed immediately by the short vowel o (for example).
ei, ou, oe, i.e., are short vowel combinations, they sound similar to the English weight, boat, and bite. The last combination is rare in Arapaho and is pronounced by saying the short vowels (above) e and i right after each other.
eii, oee, and ouu are long vowel combinations. ei is like a ei with an i added to the it, oee is like an oe held a bit longer, and ouu is like a ou with a u added to the end.