Driving into Canada to hunt is easy, but I wouldn't risk driving into Mexico unless I spoke Spanish fluently and knew “the ropes,” so to speak. Hold-ups, kidnappings and bribery are neither infrequent nor jokes down there. Best to fly in and hunt with an outfitter who knows the ins-and-outs of safe travel.
To enter either country you’ll need a passport. Apply for these at least 2 months ahead of time at your post office. VISAs are not needed. A passport is good for 10 years. You’ll also need to prepare paperwork for taking guns into either country. Again, Canada is easy. Download the form off the Internet (visit www.consular.canada.usembassy.gov/). Show up with this form and your guns at Canadian Customs, pay about $25, and you’re in. For Mexico you’ll need the help of a local outfitter who will get the papers/permits for you and handle them with government officials at the airport or border. Obey all country gun laws and retain all papers or you and your rifle might part company on the way home.