It really is a simple process.
As an example if you go to the Cabela's Canada website (and not suggesting you do, just to illustrate the process), you pick the rifle you want, add it to your cart and check out.
On check out you fill in the boxes - typical name/address stuff, and then, because it's a firearm, you put in your PAL number, Date of Birth and finish checking out - pay with your credit card and then they send it to you (UPS in their case) - comes right to your door.
Any dealer that offers "on line" buying is pretty much the same especially if they have the "cart/check-out" thingy set up on their website.
Some places like Cabela's will give you "free shipping" if you spend over so many bucks but may turn around then and charge you an oversized package fee.
Smaller dealers may have flat rate shipping.
If ordering ammo watch for the "Haz" fees.
Using Cabela's again as an example they charge beaucoup bucks for shipping dangerous goods (ammo, powder, primers). If you bought a single box of shells the Haz fees would be more than the cost of the shells.
Many of the site sponsors have far more reasonable shipping rates but no matter how you slice it you are always going to save major costs on ammo if you can shop in person (or buy so much that you can spread the shipping costs over many boxes).
So when comparing prices ALWAYS check the shipping costs. A shotgun that's 40 bucks less at the "super gun shop" but they charge 60 bucks shipping is not necessarily the best deal - so find out the cost to get it "in your hands" before you decide to mail order instead of shopping at "bubba's guns" that's a few minutes driving distance from where you live.