Thunder Bay International Airport (YQT) has direct flights from Toronto, Ottawa, Winnipeg, and a handful of other Canadian cities. Most connections go through Toronto Pearson. There is no passenger rail service — Via Rail's Canadian was rerouted away from Thunder Bay in 1990 and has not returned, despite ongoing pressure to reinstate it.
By road, Thunder Bay sits on the Trans-Canada Highway (Highway 17). It is a 14-hour drive from Toronto along the north shore of Lake Superior, and about 7 hours from Winnipeg to the west. The drive from Toronto via Highway 17 is genuinely beautiful — the Superior shoreline along the way is dramatic — but it is long, and the highway passes through hundreds of kilometres of near-wilderness with few services. Fill up the tank.
Bus service runs from Winnipeg (Kasper Transport) and from some points east, but frequency is limited and journey times are long. A car is strongly recommended for exploring the region.