The Belarussian currency is currently the Belarusian Ruble (BYR).  This should not be confused with the Russian Ruble.  The two are very different.  1 U.S. dollar is around 19000 Belarusian Rubles, but only about 73 Russian Rubles. They also have a lot of ATM machines that accept U.S. and worldwide ATM cards. Exchange rates for cash slightly differ from one agency to another, but the exchange rate at an ATM machine is determined by your bank based on the official exchange rate set by the Belarussian government. Some places in Belarus would accept Dollars or Euros, but not as many places as say China. Normal payment currency in Belarus is the local BYR, but bring in USD or EUR.

VERY IMPORTANT NOTE: Only bring new, unmarked and undamaged Dollars or Euros with you. If the paper has the slightest tear, mark or damage, it will be rejected. At least half of the notes you would normally use, will be rejected at the exchange booths. This is important to note, because you might come to Belarus thinking you have plenty of money and then once you are there find you don't have enough. This is also the case with the Visa Office at MSQ Airport - they accept only shiny new bank EUR-USD notes and no cards.  

British pounds can be exchanged in Minsk and other major cities in majority exchange kiosks. In towns you can only exchange dollars and euros. If you are exchanging GBP it is worth looking around to compare exchange rates between banks. Normally there is no a BETTER place to exchange money - the official bank currency exchange rate varies only slightly and unless you exchange a bag of notes there is no point in looking for a better alternative.

Currently there are no problems converting foreign currency into BYR and vice versa. Foreign currency is available everywhere in all banks of the country. Black market is practically non-existent. Normal exchange rates are: 1USD=18500BYR, 1EUR=20500BYR.

If you buy something expensive at a market some retailers accept dollars but at one point it was illegal and is still now.  Shops don't normally accept foreign currencies, some travel agencies do but only major ones that have a license for that.

VAT refund(TaxFree) for tourists is available in major state owned malls like GUM, TSUM, Belarus, some shops in Stolitsa mall and other places. NB: Tourists from Customs Union countries(RU, KZ, AM, KG) are not eligible for VAT tax refund

Eating and drinking is pretty cheap. In a mid range restaurant a pint of beer costs about £1-1.5. A bottle of a Moldavian wine £5.  If you buy an imported wine expect to pay as much as in the UK. If you buy imported spirits expect to pay more than in the UK. Main meal costs between £3-6. 

Food in the shops costs about half as much as you would pay in the UK, especially locally produced products e.g. meat, milk, cheese, bread. Buying anything imported deodorant, shampoo, electronics can cost more than in the UK.