You can travel to Winnipeg in several ways depending on where you are coming from.
By air– Several major carriers travel back and forth from Winnipeg each day, with Air Canada and Westjet connections from most major Canadian cities. Northwest/Delta and United serve USA destinations with direct flights from Chicago, Minneapolis, Denver, and Phoenix.
By car– You can drive here. In Canada, the No. 1 Trans-Canada Highway (east-west) provides direct connection to all major urban centres in the country. From the United States, both the U.S. Interstate No. 29 and Minnesota No. 94 (Border crossing into Canada at Emerson) connect to Manitoba No. 75 North to Winnipeg. As well Minnesota No. 59 and U.S. No. 2 (Border Crossing at Tolstoi) connect to Manitoba No. 59.
By train – VIA Rail serves Winnipeg three times weekly from both Vancouver and Toronto. You can connect to Via Rail through Amtrack or your local carrier.
By bus – There are several carriers that run buses to Winnipeg: Beaver Bus Lines Ltd, Grey Goose Bus, Greyhound Canada, and Jefferson Line.
By boat – No. You cannot travel here by boat.
Find out more detailed information on how to travel to Winnipeg at the Destination Winnipeg website.
My City's Still Breathing 
yes, you can travel here by boat. please encourage people to see ALL of the breathing river life that winnipeg takes for granted on a daily basis. for inspiration on river travel, check out websites from artists like swoon or the miss rockaway armada who incorporate performance art, music, graffiti, painting, etc into daily life.
A very good point. We were referring to getting here by boat from faraway lands of course, but there are beautiful rivers and much to see once you are here.