One of the easiest ways to hear the different pinyin sounds is to look on YouTube. The trickiest ones for me to learn were the different pronunciations of "i". Here are some videos that explain the differences:
- zhi, chi, shi, r sound a bit like English "sure".
- ji, qi, xi sound a bit like English "she".
- zi, ci, si sound a bit like the vowel at the end of "pizza""visa".
There are lots more YouTube videos about pinyin sounds.
There's also a good chart at pinyin.com with all the changes described. This table at quickmandarin.com will play the sounds for you if you click on one of them. It covers the tones as well.