Russian is my first language, so when I became a mom, I resolved that all of my children would be bilingual. I now have three kids and failed with all of them in their own way (not unlike what Tolstoy said about unhappy families). They are all definitely English dominant.
But I did do one thing right with my now eight- and five-year-olds: In addition to speaking Russian to them from birth, I also enrolled them in baby sign language classes. Not only were they able to communicate through sign months earlier than their mouths and tongues were capable of physically producing words, it created a perfect bridge from one language to the other. When I spoke to them in English (if their father was around), I signed the words. If I spoke to them in Russian (when we were alone), I signed the words. Making the same sign whether I was speaking English or Russian crystallized the point that all three–English, Russian and sign–referred to the same thing, and really helped them keep it all straight.
Here are some places where families can take baby sign language classes in New York City.