The Russian word for "is" is "есть". The infintive form is "быть" (to be). Modern Russian speakers do not generally write or pronounce it when it is used as a linking verb. Rather than "Он есть мой брать" they would say "Он мой брать". They do write and pronounce "есть" to assert that something is present or to ask whether it is present. For example: "У меня есть брат. У тебя тоже есть брат?"
Present Tense Forms
Present tense forms of "быть" other than "есть" are so seldom needed that they are all but forgotten. A few places where they are still encountered:
In the Bible:
Иисус сказал ему: Я есмь путь и истина и жизнь.
Jesus said to him: I am the way and the truth and the life. (John 14:6)
In discussions of philisophy. Here is an except from Nina Guchinskaya's translation of Martin Heidegger's 1935 lecture "Introduction to Metaphysics":
Но сегодня говорят «мы». Нынче эпоха самоутверждения масс, а не личностей. Мы есмы. Какое бытие называем мы в этой фразе? Мы говорим также: окна суть, камни суть. Заключает ли это высказывание («мы есмы») в себе утверждение наличности множества «я»? А как обстоит дело с «я был» и «мы были», с бытием в прошедшем? Ушло ли оно от нас? Или мы есмы как раз то, чем мы были? И не станем ли мы как раз тем, что мы есмы?
But today we say "we". This is the era for self-afirmation of the multitude rather than the individual. We are. To what sort of being do we refer by this phrase? We say also: The windows are. The stones are. Does the utterance "We are" imply that there is a multiplicity of "I"? And what about "I was" and "We were", what about existence in the past. Has it left us? Or is it that we are that which we were? And is it not that we will become that which we are?
When a poetic or archaic effect is desired:
О, брат, где ты еси?
O Brother, Where Art Thou? (film title)
Avoiding "Is"
The word "is" is a favorite of English speakers. They have found ways to express all sorts of ideas by using "is" to attach labels to things are by declaring that they exist. For example:
The meeting is in that building over there.
To a Russian speaker this sounds odd. He might say:
Собрание проводится в этом здании вон там.
Notice that rather than declaring that the meeting is he has chosen a 'real' verb. He says that the meeting "is being conducted".
Another 'real' verb you can use is "представлять":
Терроризм представляет угрозу мировому сообществу.
Terrorism poses a thread to world society.
When to Use "Является"
You asked about "является". This is another 'real' verb which can be used instead of "есть" in certain cases. The word that comes after it is always in the instrumental case. The word "является" has no exact English translation. It literally means "to appear on the scene as" something. It conveys the idea that under the circumstances which exists, one person or thing acts in a particular role.
We can change change the last example to read:
Терроризм явлается угрозой мировому сообществу.
It is hard to translate this literally in a way that makes sense. This may be close:
Terrorism is on the scene as a threat to world society.
Though in English "is a threat", "poses a threat", or "constitutes" a threat, are good ways to express this idea, they are different expresions. None of them is a translation of "является".
For example:
Кто является директором этого завода?
Who is the director of this plant?
Он сообщил что сосед является террористом.
He informed that his neighor is a terrorist.
Russian speakers often use "является" instead of "есть" in these sentences because "is" here conveys something more than mere existence. A suit may simple be navy blue, but being a director or a terrorist involves more. They have to be on the spot and do what directors and terrorists do.
Conclusion
Most of the time the word "есть" should be ommited. It is sometimes used for emphasis or clarification.
Observe skilled Russian speakers. Note their use of 'real verbs' instead of forms of быть. Fight the urge to constantly say what things "are".
Watch for uses of "является". Get a feel for when people and circumstances are seen as "showing up" in a role.
Which languages does Russian share roots with; did Russian always have "is" and when did it lose it? It's a really interesting topic to me.
Of course I could search around on the internet, but the people here seem to know everything about everything, so you know, well... )))
– VCH250 Apr 09 '15 at 19:30