For most of the accent and pronunciation of vowels you can use most Spanish speakers as a model. The vowels have 5 distinct sounds: A,E, I, O, U. Do not use most native speakers of English, who pronounce those vowels in too many different ways. If no Spanish speaker is available, as a general rule A is close to a in cat, e is close to e in pet, i is close to i in pin, o is close to o in hope (called a long o technically) and u is something like u in dude (a long u). Do not sneak an unneeded y sound before the u. In English we say music, which phonetically might look like /myuzik/ The Esperanto word is "muziko" and has no Y sound in it . These vowel descriptions would be based on a New York City accent.
Added on March 7th, by Enrique:
As any other language, you speak Esperanto after you have learned it. Esperanto is the easiest language to learn. For examples please go to:
Listen to a 2-minute conversation: http://esperantofre.com/gerdakd/gerda03.mp3
10-minute Video: http://www.youtube.com/watch?v=X9KI5rr4wa4
Learn Esperanto: I will help you finish the basic course in less than 20 hours: http://esperantofre.com/edu/lernua.htm