It is a good idea to ask for an application well in advance of requesting the letter of invitation. In most Western countries there is a Belarusian Embassy in the capital city. In the U.S. there is also one in New York. Use the one in New York. The visa will be issued and affixed to your passport.
Different Embassies appear to charge different fees for different levels of service.
The faster you want your visa the more it costs. We are compiling the different tariffs and will post them here once they are verified. If you are going to be in Belarus from the 15th to the 20th of the month apply for the 10th to the 30th. This will avoid any problems if you have to extend or delay your stay. It gives you flexibility.