I have gotten this question several times and thought that I would just cover several different methods and let you choose which works best for you.
The first way is to use a SleepEZ Springhook. They are easy to screw and unscrew and will stand up to the nastiest coyote. I personally like and use the 2" on coyotes on down to raccoon but some feel that is smaller than they like and will go up a size.
Another method is to use the Quick Links. They are strong and hold well but they are not quite as easy to screw and unscrew as the SleepEZs.
You can use either the HD Split Rings or the Mini Split Rings as well. They work just like a keychain to get the items connected but I have heard of people having coyotes pull both the mini and the HD apart so to be safe I would double up.
Lap links are also and option but they would need to be welded to ensure full closure and that seems unnecessary given that there are options that are easier to work with.
You can also just run the loop on the cable through the swivel and then pass the stake end through the loop. It's cheap and will do in a pinch but I prefer using something that allows the stress to be put on the loop of the cable stake instead.
So as you can see there is no one "right" way to connect a trap or snare. My advice would be to try a few of each of these systems and see what works best for you then buy the quantity that you will need.