There are a whole bunch of weird quirks that we can skip over: the details of the law honestly take weeks or even months of study because there are lots of little non-obvious things. Still, you can get 90% of the regulations with this:
- Rifles and shotguns are 'non-restricted'. You can carry these in the passenger seat of your car or over your shoulder if you like. If you leave your gun in your car, make sure it's out-of-sight. When you go to bed just remember to take the bolt out and toss it on the floor beside the unloaded gun and you're not doing anything illegal. Everyone is more responsible than this, but that's the legal requirement. These firearms are not tracked by the government.
- Short barrelled rifles and pistols are 'restricted'. You can only use these at shooting range, can't take them anywhere but to the range or gun smith, and have to transport/store them behind two locks. Unlike 'non-restricted' firearms, 'restricted' guns are registered to a particular owner and the government keeps track of who owns them, though you can lend them to friends if like.
- Machine guns and very small pistols are prohibited but if you owned one 20 years ago or you inherit one from a family member then you can have it. There's no other way to get a license to get one of those.
- Things like airsoft, crossbows, bb guns etc. don't count as firearms. Neither do 'large bore' weapons (like a 6-pounder cannon) and guns made before 1900 (e.g. Colt Single-Action Army). Anybody can own those and do whatever they like with them: there are no regulations on them but finding one is hard. I've been after an M203 40mm launcher just to say I have one but they're rare and expensive ($5000+). Everyone is more responsible than carrying a grenade launcher around. In principle you wouldn't be breaking a law but that won't stop you from ending up in court and wasting money before being found not-guilty.
- Magazines for centre-fire guns are restricted to 10 round magazines. Rim fire and manually cycled guns don't have that restriction. (roughly, again there are some quirks and loopholes but that's good enough for a first approximation).
Depending on whether you want non-restricted or restricted guns you'll need to have an appropriate license to own them legally. Each license requires a ~2-day training corse, a written exam and a couple of practical exams. The content of the course includes your legal obligations, safe handling, basic functioning of firearms, ammo, ballistics, and some info on how to shoot. The purpose of the course is safety, not making you an expert marksmen or hunter. The paperwork for a license costs around $100 to file, looks a lot like a citizenship application, takes a minimum of 45 days, and includes a criminal and mental-health background check along with some additional things like checking with your ex-wife and making sure you haven't been fired lately.
Assuming your license is granted you'll have a criminal background check run every day for the rest of your life and if you're suspected of violent crime (or reported for suicidal behaviour, etc) you can expect a visit from the police and they'll take your license/guns until you're cleared and back in good standing. As you can imagine this sort of arrangement leads to the bizarre fact that licensed firearms owners in Canada are less likely to shoot another person than a cop and are 1/3 as likely to be charged with any crime than a 'normal person'. It makes sense when you consider what a pain it is to get a license and the fact that it's expensive enough to keep 'poor people' out of the hobby which skews the demographics. Owning guns doesn't make you a 'safer' person, but only 'safe' people can legally own guns here so the statistics reflect that.
Once you have a license, you present it to a store and can buy whatever category of guns you're licensed to own. You can also buy ammo, and certain kinds of explosives with that license too. That license also allows you to teach other people to shoot, work in gun stores, manufacture/3d-print firearms from scratch, buy/sell and import (though the USA has additional restrictions on export so it's not that easy and most people use a broker) too. Every 5 years you have to renew the license.