Anyone can now bring $3000 into or out of the country without declaring anything at customs. If it is about $3000, but below $10.000 you need to declare it, but there is no problem. If you are bringing in or out more than $10.000 then you do need to show the source of such funds.
In the past, you had to declare everything; the limit was just $300; you were not allowed to bring rubles in or out; and even minor violations risked fines and or confiscation. This is a very positive step in the right direction for Russia.
I always suggest you carry some cash, just in case. There are exchange booths everywhere and their bid offer spread is better than anywhere else in the western world. However, the best way to get rubles or dollars is to use an ATM, which are also almost everywhere. And, it will be cheaper to buy your rubles onshore than at home.
If you need to use Western Union or one of their competitors to get cash, remember it will cost you up to 10% in commissions, which unless you are broke and desperate, it is much better to use your credit card. Please keep in mind that most banks are closed on the weekend, and not every bank will give a cash advance against a credit card. Naturally, you must have your passport for identification, too.Always be careful when using an ATM. Protect your password, and make sure no one is taking too great an interest in how much money you are withdrawing. I personally do not like sticking my credit card into a cash machine, just in case it gets eaten. Something to think about if you are planning to leave the country in less than a day, and you won't get your card back for several business days (if at all). A bank card is much better, as it can more easliy be cancelled, and then re-issued.
Like driving my car on a full tank, I prefer to get more cash before I run out. Cash is still universally the preferred method of payment in Moscow, although in emergencies, you will survive on credit cards.


