There are severals ways depending on desired effects to tie your line onto a lure. Often times I will use a swivel and clip. However there are times that I will prefer to tie directly onto the lures as well. That may mean tying onto a split ring. However I've choosen another method. I will slide onto it a swivel instead. A little less hardware on the lure.

Rapala Floating Minnow size 9 with swivels threaded onto front split rings.
Then there's the loop knot that sometimes makes for good lure movement and without the use of a splitring. I however do not like to tie a loop knot with my direct line. I feel that often times, the light line that I use results in a weak spot on the loop. So I opt to use a higer strength test line and tie a loop and leave that on the lure. Then I will attach my main line onto the loop. I typically will tie a nail knot onto the loop line over both lines and using the loop knot to anchor.

Rebel Pop-R's with a 30 lb mono loop line tied on.