Fraud is a huge risk with any international clients. Many sellers simply limit the list of countries, to which they ship, for their own safety. You can always refuse orders to customers in the ex-USSR, which is actually 15 different countries and 3 of them are now in the EU.
In the last couple of years, several businesses were created to circumvent this protection because ex-USSR consumers want goods from the USA for many reasons. Immigrants from some of those countries who live in the USA place orders for domestic delivery, pay with the US accounts, ship the products to the final destination, and collect money from the consumer. This way the risk to US e-tailers is minimized because they're dealing with US entities that are subjects to US laws (unless they flee the country).
The main problem with e-commerce in ex-USSR isn't payment systems, which are abundant, but delivery methods. The government post is unreliable and international courier services, such as UPS and TNT, are too expensive. As a result, some regions have no access to major e-tailers and others have peculiar methods, such as a "local distribution center" where all orders from the city come in X times a week & customers come to pick them up.
As for payment methods, they vary from country to country because banking systems & regulations are different. The top three are:
- Cash to the courier at delivery
- Debit card payment
- E-payment solution, such as Yandex.Money, Qiwi, and WebMoney
Some e-tailers also support direct wire transfers and "money orders" (similar to Western Union but done through the state post).