Airport departure taxes are almost always included in the price of the airline ticket. Hotels charge an 18% value-added tax if you pay in cash or by credit card upon arrival; if you pay in advance, then you don't get charged these taxes (at least that's the general rule). Moscow hotels add an extra 1% tax to your bill.
Russia's 18% value-added tax (V.A.T.) is charged on most everything and refundable on almost nothing (interestingly, the V.A.T. law specifically says the V.A.T. doesn’t apply to exported goods, but there's no mechanism worked out for handling refunds at the airport, nor do stores have V.A.T. refund forms). Goods bought at duty-free shops in the airport are free of V.A.T.