The following countries do not need a visa for entry up to 330 or 90 days.
Armenia, Azerbaijan, Brazil, Cuba, Ecuador, Georgia, Israel, Kazakhstan, Korea (Democratic People's Republic), Kyrgyzstan, Macau, Moldova, Mongolia, Qatar, Russia, Serbia, Tajikistan, Turkey, Ukraine, United Arab Emirates, Uzbekistan and Venezuela.
Belarus can be visited for 5 days visa free by visitors of the following countries; Albania, Andorra, Antigua and Barbuda, Argentina, Australia, Bahrain, Barbados, Belgium, Bosnia and Herzegovina, Brazil, Bulgaria, Canada, Chile, China, Croatia, Cyprus, Czech, Denmark, El Salvador, Estonia, Finland, France, Germany, Greece, Hong Kong, Hungary, Iceland, Indonesia, Ireland, Italy, Japan South Korea, Kuwait, Latvia, Lebanon, Liechtenstein, Lithuania, Luxembourg, Macao, Macedonia, Malaysia, Malta, Mexico, Micronesia, Monaco, Netherlands, New Zealand, Nicaragua, Norway, Oman, Panama, Peru, Poland, Portugal, Romania, Saint Vincent and the Grenadines, San Marino, Saudi Arabia, Seychelles, Singapore, Slovakia, Slovenia, Spain, Sweden, Switzerland, UK, USA, Uruguay, Vanuatu and Vatican.
Nationals from Gambia, Haiti, Honduras, India, Lebanon, Namibia, Samoa and Vietnam may obtain a 5 day visa if they have a valid Schengen visa(with entry stamp) and confirmed departure tickets from Minsk airport.
For the 5 day visa you will need at least 25 Euro for each day of stay plus proof of medical insurance worth at least 10,000 Euro. You must enter and exit through Minsk airport. It is not valid for arrivals or departures from Russia. You can buy insurance at the airport for 6 Euro.
Everyone else has to get a visa in advance and you probably need an invitation/tourist voucher. You can get a visa on arrival at Minsk airport if you have an invitation that you have organised in advance.
A transit visa may be easier to obtain but it may be more expensive depending on your passport.
Full story on Visa requirements
Belarus 5 day visa