Having in Russian is expressed with the preopsition у + the owner in the genitive case + the object owned in the nominative case.
Below are the forms of the personal pronouns in the genitive case. In Russian the letter is added to pronouns that begin with a vowel (его, её, их) and are precedeed by a preposition (у):
Nominative
Genitive
I
я
меня
you (sg.)
ты
тебя
he, it
он
него
she
она
неё
we
мы
нас
you (pl.)
вы
вас
they
они
них
In English you can use the verb to have not only to show possession, but also to say something about the object or person that you 'have'.
When you say I have a car, in English you indicate that you are the owner of the car.
When you say I have the car, you don't necessarily indicate that you are the owner of the car. The car may belong to someone else; you are using it only temporarily.
When you say I have an old car, the emphasis is not on the fact that you are an "owner" of a car, but that it is old. In fact, the listener may already be aware that you do have a car, and only wants to know what kind it is. This sentence can be an answer to the question, What kind of car do you have?.
In Russian, when the emphasis is on the fact that you are the owner of something, you would always use the word есть:
У меня есть машина.
If you want to say something about the thing or person that you "have", you would omit the word есть:
У меня большая машина.
This sentence translates as I have a big car, with the emphasis on the kind of car you have. Another good way to translate the sentence is My car is big.
When a Russian asks:
У тебя есть машина?
he wants to know if you "own" a car. This is why he would use есть in the question.
When a Russian asks:
У тебя большая машина?
he wants to know if your car is "big". He already knows that you do have a car.
If someone asks in English if you have something, one possible way to answer in the affirmative is with I do. The Russian equivalent is Есть. The Russian equivalent of the negative I don't, is Нет.
The preceding examples show that Russian equivalents for to have don't always use есть.
As you translate English expressions with to have, always ask yourself whether "possession" is questioned, or something else. If possession is questioned, always use есть.
Also, you should always be careful not to put the person who is the "owner" of something in the nominative case.
This confusion stems from the fact that in English the "owner" is the subject of the sentence: I have a car. In Russian, on the other hand, it is the object, or person "owned", that is the subject of the sentence, and therefore in the nominative case:
У меня есть машина.
In Russian, the owner will be in the genitive case, preceded by the preposition у, as in the example above.
Past Tense
The past tense of есть is был, была, было, были. The verb agrees in gender and number with the thing one has. У меня была японская машина. У меня были русские книги.
The question word что when used as a subject of the sentence will require the neuter form of быть in the past tense. Что у тебя было вчера?
The non-existence, or absence, or not having something in the past is expressed with не было and the genitive case. У Виктора не было компьютера.
У нас не было чемодана.
В этом городе не было музея.
В нашем доме не было телефона.