Okay, if you don't know how to get here, the rest of our information is kind of moot.
Rental cars are available at each airport.
A good way to see the state is to fly to Montana, rent a car and do a loop tour. Amtrak serves Montana on its Chicago-Seattle line. It crosses the northern portion of the state, skirting the southern border of Glacier National Park before crossing the Rocky Mountains. Greyhound provides bus service between Montana cities and to points outside the state. Travel by auto can be quite hazardous across the state because of slick roads and freezing temperatures.