By bus
Greyhound Bus Lines (http://www.greyhound.com) operate a station in Coeur d'Alene, a large town south of Sandpoint. From Coeur d'Alene, you can take a N.I.C.E The North Idaho Community Express Bus to Sandpoint.
By plane
Sandpoint does have an airport, unfortunately it is only serviced by charter planes and even then, getting in and out is complex and expensive. If you want to fly in, Spokane International Airport GEG is your best bet. Located about 2 hours southwest of Sandpoint, it is a hub for Horizon Air, Delta Air Lines, Frontier, and Big Sky Air, and airlines like United and Southwest also fly there. Most flights bound for, and departing from, GEG leave from/go to Seattle/Portland, so be prepared to fly to Seattle or Portland even if you are heading east. You can get a flight directly to Minneapolis, but expect to pay more.
By train
Sandpoint has a small station on the Amtrak Empire Builder Line, (http://www.amtrak.com/ser...) which runs from Chicago to Seattle/Portland, and services most of the northern Midwest and Northwest. All Amtrak trains arrive and depart from Sandpoint at ungodly hours, but bunks and other accommodations are available.