Winnipeg International Airport serves the great city of Winnipeg with flights to most of Canada, the US, and the Carribbean. I don't believe they have any international flights, like they used to. :(
If you need to get around in Winnipeg, your best bet would be to rent a car, as the city is quite spread out, and our downtown (at the present) doesn't offer that much. You can also take buses for around $1.50 per trip (ask for a transfer if you need to transfer to another bus). The #11 and #21 run down our city's main thoroughfare, Portage Avenue.
You can also call a taxi if you wish, and our city has a few 'water taxis' that run down the river in summertime.