Learn the IPA symbols
English spelling is a terrible indication of a word’s pronunciation. We only have 5 vowel letters in the alphabet, but we have around 20 vowels and diphthongs, depending on which variety of English you are listening to. And to make matters more difficult, spelling reflects the etymology of the word, which means that Saxon and Latin-root words behave differently.
All of which means that anyone wanting to improve his or her pronunciation needs to study the International Phonetic Alphabet (IPA). This presentation is a brief introduction to the vowels and diphthongs.