http://vitalstats.gov.mb.ca/getting_married.html
Follow the link, it really tells you everything you need plus links to appropriate documents.
No one gets married at the courthouse. You need to find a registered marriage commissioner, who will marry you pretty much anywhere (I would assume if you really, really wanted to get married at the courthouse, they would meet you there?).
You need to get a marriage license at least 24 hours before getting married.
You marriage certificate will be issued once your marriage paperwork is sent away and processed by Vital Stats in Winnipeg.
You [i]might[/i] get a copy of the registration for the officiant, but usually that's not good enough for most things. I say might because when we got married 10 years ago you did, but when our youngest baby was born last year they had revamped the birth registrations so you don't get a copy anymore, so I assume the marriage registration form is also revamped in a similar way.
You will need to apply to VS to get your certificate, it can take anywhere from a couple of weeks (if they rush) to a couple of months.