If you were to ask a native English speaker how many vowels exist in the English language they would probably tell you that there are only five vowels: A, E, I, O, U. This is what native English speakers tend to be taught at school.
In reality 20 different vowel sounds exist, made up of short vowels, long vowels and diphthongs. These vowels sounds can be represented using the International Phonetic Alphabet.
As native English speakers, we tend to read words and names based on our memory of how we remember hearing it. At school we are drilled with spelling tests and dictation. Perhaps that's why we can get by without the International Phonetic Alphabet. However, this is also why we have difficulty pronouncing unusual names and words that we aren't familiar with. The letters give us a vague representation of the pronunciation and we have no audible memory to refer to.
My advice for non-native English speakers is to learn the phonemes of English based on the International Phonetic Alphabet and develop their audible senses that are based on memory and experiences. The former is a logical process and the latter is based on immersion. In language learning utilizing a logical approach combined with an immersive experience is essential for achieving results.
The 20 vowels sounds in the International Phonetic Alphabet are represented as follows: