Hello, dear student!
Today I would like to give consideration to one of the most disputable topics for foreigners - about our writing. I often notice puzzlement of people, who learn Russian, - why we write the letter "ё" [yo] instead of "е"[ye]. What should we do in order not to get confused because of another option of writing in a dictionary? Let's analyze this fact.
If you want to get to know about the origin of the letter "ё", you should turn to history and the information about Russian princess Dashkova, but I will not describe this story because it is unnecessary here. I would like to find out the proper way of solving this mishmash for foreigners. To get accustomed to such words, for a start I would begin with learning textbooks for children, because all words are written there with the letter "ё" as it is also difficult for children to understand where is "Ёлка" [Yolka], and where is "Ель" [ Yel']. Sometimes, you can even see the words where it is proper to use both of these letters, i.e. you can read "блеклый" [bleklyy] and "блёклый" [blyoklyy] and it would not be a mistake. As in Russian culture, as in literature, author decides on his own whether to use the letter "ё" in his works or not. Thus, it is not easy enough for beginners who learn Russian. For example, there is almost always the letter "ё" in the works written by a Russian writer Alexandr Solzhenitsyn. Probably, it's caused by the fact that the auditory of his readers includes not only Russian speaking people, so they have decided to make the understanding of his texts easier. Unfortunately, there is no certain rules on learning the letters "ё" or "е", thus even Russian speaking people often make mistakes, using this or that word incorrectly. But there is category of words which you should learn and memorize the usage of these two letters in writing:
Безнадёжность [Biznadyozhnast'] - hopelessness
This word means the situation, when there is no hope anymore and you cannot fix the situation
Блёстки [Bljostki] - sparkles
These are sparkling little things which you can often see at parties or on dress
Боксёр [Baksjor] - a boxer
A sportsman who takes boxes lessons
Бритьё [Britjo] - shaving
The process of removing hair from the skin with the help of a razor
Василёк [Vasiljok] - a cornflower
A sort of a field flower
Алёша [Alyosha] - Alyosha (a Russian name)
Козёл [Kazyol] - a goat
Name of a horned animal
Ребёнок [Ribнonak] - a child
A little human
Счёт [Shchyot] - a bill/invoice
Some words which are read and pronounced only with the letter "е"
Ева [Jeva] Eve
Медвежонок [Midvizhonak] - a teddy bear
A bear's baby
Свежий [Svezhiy] - Fresh
Ready to be used, not old
Все [Fse] - All
Plural form,for example, if we talk about a group of people
Do not mix it up with the word "всё" - when we talk about inanimate objects
Черти [Cherti] - devils
Do not mix it up with the singular form "чёрт" [chyort] - devil
It is only a short list of the words with the letter "е" and "ё". If you want to know writing and pronunciation of these words better, I recommend you to learn the words which are written correctly in Russian dictionaries.