It's not legal to use US dollars or Euro for transactions in Russia. However, you'll still see a lot of prices marked in Y.E. (which means "units" and usually equals the current US dollar or Euro rate).
That is the relic of the 90s, when hyperinflation made it impossible to put the prices in rubles. However, you will still have to pay with rubles in most cases. Generally, foreign currencies are usually used for "under-the-table" transactions, which are not going to be declared.
So, you won't be able to use US dollars, Euro, or any other currency in a shop, cafe, or to pay to a service provider, unless he is OK exchanging it on your behalf.
Having said that, many Russians still have their savings in US dollars or Euro, partly because of the old tradition, partly because many get their salaries in foreign currencies, partly because they still don't trust in Ruble's stability, so you'll often find that you'll be able to pay to a private person with US dollars or Euro (depending which currency this person trusts better).
It's better to have some cash ($200-400 US - just enough for initial expenses - transport, accommodation, food) when you come to Russia and the rest – on your credit card.
If you're going to small towns, cruises, tours or to the countryside, it's better to take cash only, because you might have problems cashing the cards or travelers' cheques.
Cash. is used much more often than the cards, and if you're outside of the big cities, take cash only because it will be hard to cash the cards or cheques.
It's better if the cash is in US dollars or Euros, because that's the currency you'll be able to change everywhere in Russia.
Also Euro is strong at the moment, and many Russians are transfering their savings from Dollars to Euro, so you're likely to get a better exchange rate (see the current exchange rates in the right column of this page).
If you have any other currency, then it might be hard to find an exchange office, and the rate won't be in your favor. Better change your money in US dollars or Euro beforehand.
Also, the exchange rates of $ US and Euro to the Ruble is better in Moscow and St. Petersburg. If you change your money in Siberia, for example, you'll lose about 3%.
Travelers' Cheques is probably the most secure way of keeping your money: you are the only one who can cash the cheques and if lost they can be reissued - just write down the numbers beforehand and keep them separate from the cheques.
The problem is that in Russia you can refund them only in banks, which are opened only from 9 until 17. The banks charge commission for refunding the cheques (about 2-3%) and for buying the cheques - usually 1%.
The most widely accepted cheques in Russia are American Express and more rare - Thomas Cook. In the Practicalities sections of our city guides, we provided the addresses of banks, which accept AMEX, Visa, Thomas Cook and other cheques. Their commission rates are usually 2 to 3% for cashing.
Please, note, that you cannot pay with travelers cheques in Russia, you can only withdraw money from them in banks.
Also, the recent customs regulations make it necessary to declare the cheques when you enter Russia.
Credit Cards. There're many cash machines in Moscow, St. Petersburg and major Siberian cities, and a lot of shops and restaurants accept cards in the big cities. However, as soon as you go to smaller towns, you'll find it hard to use your credit card.
If you don't know where to look for an ATM ("bankomat" in Russian), go to any big and expensive hotel. However, it's better if you withdraw your money in the cash machine, which is at some bank's office, in that case if your card gets swallowed you'll deal with the problem faster.
See banks and cash machines (ATMs) addresses in Practicalities section of the city guides.
Usually banks charge 0 to 1% commission if you withdraw money with the card of the other (foreign) bank, but your bank - the issuer of the card - will take from $2 to $5 US for this operation.
In most of the cases you'll receive rubles, some ATMs dispense rubles as well.
Visa, MasterCard are accepted almost in any ATM, Visa Electron and Cirrus / Maestro - more rarely, and AMEX and Diners Club owners might have problems cashing the cards.
Travelers' Cards are the plastic cards that are a mix of traveler's cheques and debit cards - you can cash them in the cash machines. Visa Travel Money traveler's card can be shared by many people (there can be many cards for one account) and if stolen it can be easily reissued. For more info go to http://www.visa.com/vtm/.
Visa Travel Money card works like this: you pay $5 US to open this card, put an one-time amount (you can't put more later), use all money on this card and then chuck it.
This card can be used by anyone who knows the PIN, everytime you withdraw money, there's a comission of $5 US.
The good thing about this card is that all money are on the Visa accounts, you can always phone Visa numbers to know how much money you have left on your account and in case you loose this card, it's easier to re-issue it (and it's only $5), and Visa cards are accepted almost everywhere.
Also this card might work well if you want to pay for something.
Instead of writing a check, sending your credit card data etc., you can just go to any bank, buy this card for $5, put some money on it, send this card by post, send a PIN via email, a person receives this cards, receives the PIN, goes either to a bank or a cash machine and gets money. After this the card can't be used anymore.