How I USED to do it:
-With spoons like Gibbs Crocs that have a split ring and crane swivel from the factory I would tie it right to my mainline and fish it like this with no issues. However each time you want to try a new lure you have to cut + retie
-With spinners that have a swivel built into it I would tie right to the mainline same as above with no issues.
-With spinners like Blue Fox I would tie right to the mainline with no swivel, however at times I noticed I was getting some line twist.
How I do it NOW:
-On my one spinning rod that has 12 mono mainline. I tie a crane swivel to the mainline and then connect a DUO-LOCK to the swivel. This is basically the same as using a snap swivel but IMO the duo lock is much stronger than a snap swivel. On all my spoons I REMOVED the split ring and swivel. I just put the big end of the duo-lock though the eye of the spoon, close, and ready to fish. If I want to swap lures which I do often it takes 2 seconds.
-On my other spinning rod that has 20lb Suffix braid as the mainline I don't want the braid connected right to the lure (scare the fish IMO). So I put a bead through the braid that won't go through the top eyelet, then tie the braid to a crane/barrel swivel, then run a 3ish foot mono leader, then put JUST a duo-lock at the end of the leader (no need for a swivel as well as there is one on the mainline). Then, like above, I just snap/un-snap the duo-lock to change lures.
With this set up I like that I NEVER have to cut line and tie knots. Oh and if I have a spinner with a swivel built in to it I cut it out with a pair of side cutters.
To some this may seem overly complicated but I like tinkering with my gear and finding way to fish smarter, not harder