There are no to be verbs (am, is, are…) in Russian.

Usually the verb "to be" (быть) is used in the future and past tenses only. It is omitted in the present tense. E.g. Я был худым. - I was thin. Я толстой. - I am fat (notice the verb is absent here) Я буду худым. - I will be thin. The only present tense conjugation of the verb is "есть" which roughly translates to "there is". This is most commonly seen in the Russian construction for having something e.g. У меня есть телефон. - I have a telephone, or more literally translated "At me there is a telephone". Hope this helps! If there are other scenarios where you are unsure, just let us know!

The only form of быть used at the present is есть, that is the equivalent of "there is" in english. For exemple, На улице есть машина: there is a car in the street. есть is also used to express "to have" in the structure y+genitive+есть: У вас есть машина? : Do you have a car (litterary: By you is a car ?)

thanks Arnaud ...

The verb "to be" быть, is not conjugated at the present tense. The exemples that you've given are: infinitive, past, conditional. Я русский парень, is the present tense, and the verb быть is implied. There are other verbs that can be used (with a lot of precautions) like бывать, являться, существовать,etc...to replace быть in precise contexts.