This is a very pleasant town with a nice pedestrian area and central square worth a visit if you are in Belarus, but it may remind you more of western Europe than the former Soviet Union until you get out of the centre.
Domestic trains from Minsk are daily, departing 4:22PM taking five hours, with several night trains.
There are several international trains from Russia, the one from Moscow is daily and for a 16 h journey. From Saint Petersburg there is up to three departures a week taking 22 h. During summer additional routes are added, Odessa (39 h) via Kiev, Simferopol (37.5 h) and Sochi (62 h). From Poland, you can take train in Białystok. There is two direct trains per day, at 06:50 AM and at 19:02 PM. A ticket is about 20 zlotys. It seems train times have changed, there is now (also?) a train leaving around 11:00 am from Białystok.
Note that cigarette smuggling is very common, and many people will be doing it.
There are a lot of buses from Minsk (costs around 45,000 rubles for the express route, which takes 4 h) from Vostochnyj Station or from Druzhnaya Station (behind the main train station), few from Brest (the same price), few from Vilnius, one bus from Warsaw (departure around 10-11 a.m. from Warszawa-Stadion station; a few buses from Moscow.
There are plenty of buses and trolley buses going around town. In the evenings though, they get down to travelling on the outskirts iblt once an hour or two. A ticket for a trip costs 1300 rubles ($0.20 US). Buy the tickets from kiosks near the bus stops. If you speak no Russian, just say "Talony," and hold up fingers to indicate how many.
When you get on the bus, find a grey metal device that they have near the windows, put your ticket in and clamp down on it with a little lever next to it. Then, it is validated and if a ticket controller comes in, you will get no fine.
Taxis are cheap and plentiful: taxi trips within the city cost about 8000 rubles.
Retro Pizza, 31 Sovetskaya St (Follow the long pedestrian street down from the main square. Near Lenin Square). Good pizzas here. The menu is only in Russian, but some staff speak English, and some dishes (not the pizzas) have pictures to point to.edit
Pizza Kofe, 15 Kirova St, ☎ +375 15 272 2229, . Good pizza and poor coffee.65000 BYR for medium pizza and 85000 BYR for big one. edit
Hotel ** Semashko, 10, Antonov str. (100 metres up from the bus station), . checkin: 12:00; checkout: 12:00. The hotel is very nice, right up to "western" standards. It has air conitioning, and everything is clean and modern. There is a pool in the hotel. The location is very convenient: when you get off the bus, look for where there is lots of traffic, walk up there and cross the road: that is Semashko, about 100 m up. Some of the service was a little bit less than ideal, but nothing is out of the ordinary in this part of the world.About $83 for a 'superior room'. edit
Neman *** Hotel, 8, Stefana Batoria Str. (Sovetskaya Sq.), ☎ +375 152 79 17 00, . The modern hotel located in the heart of the city has 69 fully equipped rooms: conditioning, 32-inch LCD TV-set and cabel TV, modern furniture, ortopedic bed, telephone, bathroom with shower/bathtub, additional black-out curtains, hair-drier, refrigerator, kettle, mini-bar. There are also Wi-Fi and secure parking, restaurant "Neman" and pub. Hotel proposes weekend discounts for staying on Friday, Saturday, Sunday.Daily rates: Standard SGL room - from $52 / €43, Standard DBL/TWN room - from $75 / €58. Breakfast is included in the room rate. edit
Slavia *** Hotel, 1, Molodyezhnaya Str. (close to Sovetskaya Sq.), ☎ +375 152 77 35 35, . Mini hotel has 22 comfortable rooms: individual conditioning, LCD TV, telephone, bathroom, mini-bar. Other services: Wi-Fi, secure parking, cafe, in-room dining. Hotel offers 10% discounts for staying on week-end.Rates by request, breakfast included. edit
Tourist *** Hotel, 63, Yanki Kupaly Pr., ☎ +375 0152 56 99 48, . Hotel is located behind the Neman river, 15-20 min to city center. 152 of comfortable rooms are well-appointed with TV, telephone, bathroom; classic interiors. Hotel sevices: High Speed Internet Access, restaurant "Tourist" with European and national cuisine, express-cafe, dental office, solarium, massage room, currency exchange office, hairdresser and a business center.edit
Kronon Park ***** Hotel, woodland Pyshki, ☎ +375 152 73 98 00 (info @ kronon.by), . All rooms are equipped with telephone, mini-bar, personal safe, LCD/plasma TV, hair-drier,fluffy bathrobe and slippers. High speed Internet access in the lobby.Standard room is from 135USD/103EURO. The price includes breakfast, VAT and all fees. Swimming pool and sauna are free of charge. edit