There are several vowels in Russian which do not have their own sounds. These are the letters "Е" - [E], "Ё" - [YO], "Ю" - [YU], "Я" - [YA]. They are denoted either with the combination of two sounds or with the soft sound "й" - и краткая [i kratkaya] or they sound like [э] - [eh], [о] - [o], [у] - [u], [а] - [a], accordingly.
1. They denote two sounds [й'э] - [ye], [й'о] - [yo], [й'у] - [yu], [й'а] - [ya] in the following cases:
In the beginning of a word. Юла [yula], ель [yel'], ёж [yozh], яблоко [yablaka].
After a vowel. Таяние [tayan'ie], каюта [kayuta], маёвка [mayofka], поединок [payed'inak].
After separating letters "ъ" and "ь". Подъёмник [padyomn'ik], серьёзный [sir'yoznyy], вьюга [v'yuga], пьяный [p'yanyy].
Note. If the letter "И" is after soft sign "ь", it is also pronounced like the combination of the sounds [й'и] - [y'i]. Муравьи [murav'y'i], воробьи [varab'y'i], ничьи [nich'y'i].
2. They denote the sounds [э] -[eh], [о] - [o], [у] - [u], [а] - [a], if they stand after the consonant sound which is a part of the sound-pair according to hardness-softness. Then the letter "е" [e] expresses the softness of a previous consonant and sounds like "э" [eh].
День - [D'ehn']
It might be difficult for you to pronounce words with the letters "е", "ё", "ю", "я" depending on your native language. Not everybody can convey the sound "й" [y] which softens the sound "э", "о", "у", "а" so you get "лублу" [lublu] instead of "люблю" [l'yubl'yu] (love).
To pronounce these sounds, you should practise the hardness-softness of consonants.