If you are a bilingual person, then it's not a problem at all. All you have to do is just to translate names, geographical locations, such as city, district, region, country, place of registration of a child, etc. The most important thing when translating a birth certificate is to make sure that all the names are spelled (or transliterated) the same way they appear in all other official documents. This can be a big problem for the immigration service if this rule is not followed. For example, the name Aleksandr can be spelled in several ways, like Alexander, Aleksander, Aleksandr - you got an idea. If you do not have your name transliterated yet, chose one spelling and go with it in every document.
If you are not sure how to translate your place of birth, wikipedia is a good source of geographical information. Let's say your birth certificate states that you were born in город Винница, Винницкой области, УССР. There are several options you can chose from - city of Vinnytsia, Vinnitsa, Vinnica. It all depends on how the city was recorded in your other documents. Then goes the region which should be the same - Vinnytsia, and finally, Ukrainian SSR should do it for the republic you were born in. Please don't be confused about district and region: район - district, and область stands for region, or it can be translated as oblast.
For the USCIS purposes, all the stamps should be translated also. If the original document is old and the stamps are not readable, you can put a note at the bottom of your translation that the text in the stamp is not legible.
I think I covered the most important parts when it comes to a Russian to English translation of a birth certificate.
Though most of the time, Immigration office requests a certified translation, that means that the translation has to be signed by a professional translator. If this is the case, you can always go with a Russian certified translation performed by a professional company. If you decide to use a translation agency, make sure you let them know the spelling of your names.
Below you can see a translation of a Russian birth certificate.