As others have said, typical hunting long-arms are no problem.
When you stop to talk with the guard they'll ask you why your coming to Canada. After you tell them you're there for hunting, tell them you have a firearm(s) to declare. They'll ask you to pull over, and have you fill out a form and pay a tax. On the form you need to list the type of action, make, model, barrel length and serial number. They will look at your firearm(s) to verify this info, so have them unloaded, cased and easy to access. You can also save yourself some time and get the forms ahead of time.
My experience is that this is a very easy process. The border guards are professional and pleasant. Let them tell you what to do, and be cooperative, honest and pleasant. In areas where hunting is common, especially during hunting season, they do it all the time. 5 minutes.
Once you're done with the form and have payed the tax, they'll give you a piece of paper that needs to be on your person whenever you're afield with your gun. Make sure that whatever gun you have in your hands is listed on that piece of paper. I believe that "borrowing" somebody else's gun is frowned upon.
Handguns and other firearms the canadians classify as restricted are much more difficult to bring across the border.
If you have a successful hunt, bringing your game back to the US is also easy, but you are subject to the US customs officials. You'll have to declare your animals at the border, and fill out an import form, and of course pay another small tax.
I've only done this with deer, and only by driving. If you're traveling by air or bring back other game, YMMV.
-nosualc