Transport in Chile:

By Plane:
Many towns in Chile have airports, and domestic flights are offered by LanChile, Ladeco and other carriers, like Sky Airline. For such a long country, taking a plane sometimes comes as a relief and travelling to the south of Chile by land takes a long time, as most of the transport options go through Argentina, except boats or your own wheels.
Note that Easter Island can only be visited by plane (well, there are cargo ships) and taking a plane in Chile is almost inevitable if you want to cover large distances in a short amount of time. Also, it's the best way of reaching the Juan Fernandez Islands, although there are ferries going there, more so in summer though.

By Bus:
The major roads in Chile are paved and smooth, and bus services are generally comfortable and well-maintained. There are different classes of service. Pullman has regular seats with a slight recline, semi-cama has seats with extra legroom and seats the recline further and cama has fully reclining seats.
Distances are vast, Peru to Puerto Montt being almost 3500 kilometres for example, so it makes sence to brake up your journey a few times.
Some of the main bus companies are TurBus and Pullman, Cruz del Sur, Tas Choapa and Bus Norte.

By Train:
The State Railway Company has a few options, including regular trains between Santiago and Temuco. Still, options are limited and buses are usually just as fast, if not faster and are even just as comfortable.

By Car:
If you plan to rent a car in Chile, there are many international car rental companies operating there, such as Avis and Hertz. A local company worth checking out is Econorent. If possible, try to rent from a local company, since these can often be cheaper than the major competitors. Many won't have a website, so just ask at the tourist office for a list of local car rental companies and arrange it while you're there.

By Boat:
Running between Puerto Montt and Puerto Natales in Patagonia, the Navimag Ferry
runs through a number of channels along the coast of Chile. There are quite a few ferries offering services in the region between Puerto Montt in the north and Punta Arenas and even further south to Isla Navarino (Puerto Williams), but only on certain legs. Frequencies are higher in summer though on most routes, and some routes might not have scheduled services during winter. Routes include those between Chiloe Island and Chaiten east on the mainland, where there are onward buses to Coihaique. There are also ferries between Punta Arenas and the Chilean part of Tierra del Fuego and even a few to Puerto Williams, the southermost village in the world.
There are boats once a month between Valparaiso and the Juan Fernandez Islands and between the islands are more frequent boats. Flying is a better option to get there initially though. Even less recommended, there are irregular cargo ships going from Valparaiso to Easter Island.