Replying to Canadian government?

so i was browsing through youtube videos and a fell upon a bunch of videos of New Democratic Policy leader, Jack Layton.
so basically the point is, i started to get interested in canadian gov't because i have often felt like you guys are doing a good number of things more efficiently. i honestly didn't know that there was a queen of canada until right now so keep it relatively basic, but could some of you canucks fill me in on the roughly how the canadian government works?
greatly appreciated.