Because the English language is not phonetic, the letter "I" has different pronunciations depending on usage. For example, when referring to oneself in the first person, it is proper to pronounce "I" the same as the word "eye" or with a short 'ah' sound followed by a brief 'ee'.
Additional pronunciations of the letter "I" are based on how it is used in different words. For example, in the word 'him', the letter "I" has an 'ih' sound. This can be achieved by narrowing the width of the mouth and raising the soft palette when making an "ee" sound.
For additional video resources on the pronunication of "I", visit: http://rachelsenglish.com/pronounce-letter-2/.