By bus
Acadian Lines Bus Service (http://www.smtbus.com/) serves the entire province, and is relatively standard for a bus service. Stops on some lines are frequent, and often include very small villages - wherever you are headed, there is likely to be a bus servicing the area. That said, this does mean that buses seem to stop frequently.
By car
Travel by car is the easiest way to see New Brunswick. Recent refurbishments and expansions of the transcanada highway have left four lane highways in place across much of the southern stretch of the province. Drivers accustomed to any major metropolitan traffic will find most intercity roads to be very lightly used, even in summer months.
The roads of New Brunswick are patrolled by the Royal Canadian Mounted Police RCMP, and speed traps are sometimes in place. Speed limits have no official tolerance in them, however typically travel under 10km/h above the speed limit will not attract attention. That said, RCMP officers are not always known for their sense of humour where speeding or anything else is concerned, and tickets may be issued for any speed above the posted limits. If you are pulled over by the RCMP, typical North American rules for police interaction apply; keep your hands on the steering wheel while being approached by the police, and be respectful at all times.
As with much of Canada, winter roads are more dangerous, and travellers are advised to treat the roads with caution. Winter tires are recommended for long distance travel, however snow chains are only necessary on very rural roads and private roads. When travelling during the winter, drivers should carry an emergency kit with a source of heat, blankets, and an amount of food to ensure that being caught in a storm is only an inconvenience, rather than a life-threatening issue.
In some winter storm conditions, roads such as the transcanada link between New Brunswick and Nova Scotia can be closed due to whiteout conditions.
By train
Via Rail (http://www.viarail.ca/) provides a somewhat limited service along the Eastern coast of New Brunswick, entering the province at Aulac, and then passing through Moncton, up to Bathurst, and then from Campbellton across the border into Quebec, eventually terminating in Montreal. This service passes through the province once per day in each direction, and as such, travellers should not miss their train unless willing to extend their holiday.
Options for the trains vary, as two different types of rolling stock are in use. Standard class involves sitting for the entire journey, while a range of berths, single rooms, double bedrooms, and sitting rooms are available, depending on the cars in use. Standard class is feasible, but an exhausting option!