I think the transit system is pretty good, but I'm not one to judge since the system back home is pretty bad. I've heard complaints from locals though. Nevertheless, here is the website for Winnipeg Transit. You can access route schedules, as well as type in your origin, destination, and time of departure/arrival, and it will list a number of route options for you! (Click on the Navigo Trip Planner icon).
The cost is $1.75 for adults, and $1.55 for seniors/students. It is very accessable throughout the city. Schedules are available through the web site, at any public library, or downtown in Winnipeg Square at the transit terminal.
To go from place to place in Winnipeg, you need wheels. Rent a car! Buses only seem to come every 1/2 hour, and only run from the suburbs to downtown and back.
Avoid the rush hour - its not as bad as Vancouver, Toronto or Montreal - but why clog up the roadways for the locals.
It's pretty helpful to have a car in Winnipeg because the city is very spread out and it does get a little cold. Also you're less than 2 hours to the US for shopping, or amazing cottage country in the Kenora, Ontario area.
However if you're staying downtown you can easily get around by foot or cab.
There is the main highway 17 and highway 1 that goes through the city. They are some of the most used ways of getting into Winnipeg.
If you have your own vehicle that's great but if you haven't been there very many times you should have a map because there are alot of one way roads. If you take a taxi be sure you still have a map because if you don't know your way around the city you could be paying alot of moneyfor a tour you didn't want around the city when it would have only taken five or ten minutes to get where you wanted.