By plane
There is a small regional airport near from Vitebsk, but it is not served by any airlines worthy of note for the typical tourist, and you will be able to connect to only larger airports in Belarus and Russia. The best way to reach Vitebsk would be flying to Minsk and taking a 4.5 h train to Vitebsk. Another option would be to fly to Moscow or Saint Petersburg and taking a 9 h train from there.
While Belarus and Russia formally have no monitored border you may hop on a train and get from one country to the other, train crews normally check your passport before getting on the train to make sure you possess the visa. [Gomel airport] in Gomel, southern Belarus, accepting flights from far abroad, might be a good connection to reach Vitebsk, but you need to verify that before planning your trip.
By train
Vitebsk sits on the major train route from Minsk, capital of Belarus, to Saint Petersburg, Russia. Moscow is also easily accessible by train. Vitebsk also serves as a regional hub.
By car
Vitebsk is accessible by major highways.
By bus
Regular buses travel between Vitebsk and Minsk or Moscow, as well as to numerous other smaller regional towns. Buses to Lithuania and Latvia are also available. "Route buses" or "marshrutka" from Minsk is a good way of transportation: they are fast, convinient and can often can drop you off nearby the hotel or the house in Vitebsk, which you point to. Getting to Riga takes about 11 h by coach from Vitebsk. Getting to Moscow is around 9 h, Saint Petersburg around 12 h, Kyiv around 9 h. Note that getting to places outside Belarus by coach can be time-consuming due to border controls.