Several airlines fly to Minsk including:
When we fly directly to Minsk, we usually chose Czech Airlines as they tend to be less expensive than Lufthansa and Austrian. We have flown Belavia a few times, only between Minsk and countries in Western Europe, and have found them to be very good. We have flown on modern jets (Boing 737) and the service and food have been fine. We have never flown Belavia to the east and do not know if there is any difference. Air Baltic may be a good alternative, as their prices are usually good, but their connection times have not been convenient for us.
Flights to Belarus are expensive! Typically, you can expect to pay 2-3 times as much to fly to Minsk compared to almost any other European destination. There are rarely, if ever, discounts on flights to Minsk. The Minsk airport is approximately 1 hour from the city center by taxi. Expect to pay anywhere between $25-$50 for a taxi ride from the Minsk airport to the center of Minsk.
Do you have time and want to save money? Fly to Vilnius and take a train to Minsk. There are several low cost carriers which fly to Vilnius or Kaunas. Both are well connected to Minsk by train. A train from Vilnius to Minsk is very cheap and takes only 3 hours.
Total travel time may not be that much longer than a direct flight, because often when flying to Minsk you will have to change planes somewhere such as Frankfurt or Vienna.
Also, with the train you will arrive in central Minsk. If you fly into Minsk, you'll need to clear customs, which can be very tedious and you will still need to take a 1 hour taxi ride to get to Minsk. To get from Vilnius airport to the train station you can take a taxi (usually about $10) or a 20 minute bus ride (bus #1 departs only 1 or 2 per hour). A train from Vilnius to Minsk will generally cost under $20 (less than a taxi ride from the Minsk airport to the city) and take about 4 hours. Trains to Minsk are at least twice per day but the schedule changes constantly and can be seen from bahn.de. Make sure you have a visa in your passport, because you can not board the train without one.
It is also possible to take a bus from Vilnius to Minsk with Eurolines. Click to see the bus schedule. I prefer the train, but since the Vilnius bus station is located across from the train station, this gives you another option.
Another alternative for arrival in Minsk is a train from Poland. This is a longer ride and more expensive. The reason it is so long is that the Polish train tracks are a different size than the Belarusian tracks and the wheels must be changed.Workers actually elevate the train and exchange the wheels of the train while the passengers are inside. It is fascinating to watch, once. But this, together with border controls, causes a four-hour delay.