While Russians continue to westernize, you should to be aware of some local customs. Being late is considered normal, especially in traffic-clogged Moscow. Expect your appointments to be somewhat late (you should still show up on time, however).
If offered drinks, it is impolite to refuse, especially for men.
Russians dress up pretty much everywhere they go. Bring nice, dressy clothes with you to wear out on the town. Make sure your shoes are clean, as Russians really take care to have clean shoes, despite weather conditions.
Discussing politics used to be considered impolite, but after the 2011-2012 wave of street protests, more and more Russians are becoming involved in politics and discussing the topic is becoming less taboo. Be wary of getting heavily involved in political debates though, as some Russians may still frown upon this practice.
Expect Russians to ask you personal questions, which are often taboo in the US, such as how much money you make, and openly talk about their salaries.
Russians are not big on gender equality and political correctness. Expect men to only shake hands with men upon meeting. Casual racist, anti-Semitic, and misogynistic comments are common.