Apart from modest public transportation systems in the major cities, Idaho has no mass transit to speak of. The only Amtrak stop in the state is in Sandpoint in the far northern panhandle. Otherwise it's all driving or flying.
By plane
Flying is an expensive but wonderful way to get around and see the majestic scenery. Although many of the state's smaller airports have no commercial flights at all, while others such as Twin Falls don't have regular flights to other parts of the state, backcountry flights are available from many locations, and you get to fly through canyons and into remote airstrips that are nearly unreachable any other way. Examples are McCall Aviation and Selway Aviation in Central Idaho. If you just want to go city-to-city, call Horizon Airlines.
By car
Idaho is served by several Interstate highways. I-90 in North Idaho passes through Coeur d'Alene. I-84 enters Idaho at the Oregon border, serves the Boise metro area and passes near Twin Falls en route to Salt Lake City. I-15 serves the Eastern Idaho cities of Pocatello and Idaho Falls. The short I-86 in South Central and Eastern Idaho connects I-84 and I-15.
Most other main roads in the state are two-lane highways. In more remote locations unpaved roads are commonplace. Pay close attention to current road conditions while traveling, particularly in winter. You know you're from Idaho when your elderly grandparents think it's normal to arrive at Christmas or even just for a weekend visit after driving 400 miles through blizzards and along winding two lane river roads.
Crossing into Montana often involves going through mountain passes. This is particularly true when not on I-90 or I-15. In the winter, check with the highway department for pass conditions -- many passes are closed from the first snow until mid-April.
The two-lane US 95 and Idaho State Highway 55 serve as the only intrastate connections between North Idaho and the rest of the state. Even in ideal weather conditions, traveling by car from North Idaho to Eastern Idaho invariably involves a drive through Boise or through Missoula, Montana. Either way, you'll drive 600 - 700 miles when it's something like 300 miles as the crow flies.