The best way is came to any small belorussian village and stay there about 2-3 month. It is a most cost effective way about time and money.

First, you have to ask yourself what basic knowledge you have. Do you know any Slavonic language? If not, then it would be the alphabet. Note, BTW, that we Belarusians have extra letters in it, which you won't be able to type with your Russian keyboard layout.
 

To start learning Belarusian, first you need to have the resources to learn this language. If you don't have any resources, then learn this language with a person who lives in Belarus and knows Belarusian well.  

I'm wondering why you decided to study the Belarusian, do not share?)