Vowels can be a pain in the rear, too - we have 10 letters for them (а, е, ё, и, о, у, ы, э, ю, я), but only 6 sounds ([а], [э], [и], [ы], [о], [у]).
The trick is that there are two types of vowels - those that use a single sound and those that use two:
а - [а], я - [й'а]
э - [э], е - [й'э]
о - [о], ё - [й'о]
у - [у], ю - [й'у]
ы - [ы]
и - [и]
UPD: In Russian transcription the ' symbol indicates that the consonant is soft. Some consonants are always soft, and й is one of them.
Keep in mind that е, ё, и, ю, я always soften the last consonant that preceeds them if that tricky imp ъ not present, while consonants before а, о, у, э, ы are always hard.
Okay, in some words of foreign origin e sounds like э, as in words "менеджмент" (management), "Интернет" (Internet) or "тест" (test), but that's another story, and some people - usually elder ones - still say е instead, but it sounds wrong and funny, don't do that.
UPD: It slipped my mind last night. I have to add that when the vowel that is represented by two sounds follows a consonant, the [й'] sound is dropped, but the consonant itself is softened.
For example, words "мяч" (ball) and "меч" (sword) sound like [м'ач'] and [м'эч'] instead of [мй'ач'] and [мй'эч'].
But if there is ь present between consonant and vowel, the [й'] sound remains. For example: "вьюга" (blizzard) or "пьяный" (drunk, drunkard) are pronounced [в'й'уга] and [п'й'аный'].
The [й'] isn't dropped if the word begins with a two-sound vowel: "яблоко" (apple), "енот" (racoon), "юг" (south) are pronounced with [й'а], [й'э], [й'у] respectively.