Also, as you can see in Vera's answer, meaning for "доволен" has changed from "happy" to "pleased" (sometimes it's even more like "proud of"). So you definitely need to be more specific about the context when you need to translate "happy" to Russian because there could be different variants.
You can use "доволен" as translation for "happy" if, for example, you are curious about someones satisfaction with something:
Вы довольны результатом? = Are you happy with the result?
Вы довольны собой? = Are you happy with yourself?
But if you are translating "happy" as human emotion, than you better use words like "веселый", "радостный", "счастливый".
Are you happy? = Ты счастлив?
You look happy = Ты выглядишь счастливым.