Buses pull in at the large and bustling terminal in the middle of town close to the harbour (Diego Portales & Lillo). Many departures to cities in the north, as well as services to Chiloé Island. Cruz del Sur are the fastest, since they own many of the ferries crossing the strait and the bus bypasses the waiting line. Buses to Bariloche in Argentina takes around 7 hours.
Navimag has boats to and from Puerto Natales and Puerto Chacabuco. The latter costs Ch$ 38000 pp, Ch$ 100000 for a car. To Puerto Natales it will cost you between USD 350 (on the older ferry "Amedeo I") and USD 450 (or more, on the newer ferry "Eden"). The passage takes four days, and includes chances of viewing narrow straits, open sea and wildlife. Meals are included, beer (Ch$ 2500) and wine (Ch$ 5000 per bottle) can be bought on board. It is sometimes possible to arrange a short visit to the very remote Puerto Eden, which has this ferry as it's only link to the rest of the world (Ch$ 5000 extra).
Other companies whose name and routes change frequently have ferries to Chaiten on the carretera austral. Many departures in summer, but often only one per week in winter. The ferry to Chiloé Island leaves about 50 km south west of town, takes 30 min and cost Ch$ 1000 pp and Ch$ 11300 for a car.
Naviera Austral connects Puerto Montt with Chaiten. Ferry leaves at midnight and journey takes 10-12 hours. Simple seat costs Ch$19100, berths are two times more expensive. Check the Naviera Austral website for current schedule: http://www.navieraustral.cl
Kémelbus now has a service called "ruta bimodal" which takes passengers to Chaitén by bus and ship in a daily, 10-hour scenic trip through the fjords south of Puerton Montt.
The thousands of taxis and colectivos that bounce like ping pong balls across and along the streets are a fast and usually cheap way of travelling across town. Although you'll find that your feet will take you to most places. If walking, take extra care when crossing streets in this city. Colectivos appear out of nowhere!
You can rent a car for €28 and see the surroundings of the city.
The area along the beach near the bus station is pleasant for a walk with things along the way to entertain you. Walking east you'll get great views, especially at sunset, from the hills there.
A good place to have some seafood is at the fishing community of Angelmó. Along with the seafood market there are some restaurants. There are also a lot of options for shopping Mapuche craftworks.
There is a multitude of cheap hospedaje in Puerto Montt, so don't despair if your travel guide only shows a few expensive ones.