I just clip it on with the clip on the end of the lead rope. Coil the rope in a smallish coil, starting with the non-clip end, wrap the clip end around the coil a couple times then push the clip through the coil. And clip it to the d ring.
It works best if the lead rope is really soft and flexible. I've tried it with older, stiffer, ropes and it's marginal, at best. I actually ended up making a new lead rope out of soft cotton to it'd be easier/tighter to coil.
I posted a picture on the "Putting a bridle over a halter" thread of me and my horse getting ready to get on the trail. In the picture it shows how I coil and snap the lead rope to my saddle. In that thread my picture is on page 6 and the last post on that page. I use the ring that holds the back cinch.
Most western saddles have a leather thong to hold the ropers lariat. I loop my lead rope and lash it on with that thong.
If you don't have one. Take a piece of leather tie, attach one end near the horn with a screw and concho, In the other end put a SLIT that is large enough to fit over the horn.
Coil the lead. Make 2-3 loops around the lead with your thong, and slip it over the horn. If my lead has a snap, I usually thread the thong thru the snap you help hold that extra weight
I don't know if it will show up in this resolution, but I have my black lead rope coiled and attached in that position, in front of my right knee
I also carry hobbles with me when I ride. Usually I thread them thru the ring where the back cinch attaches and just let them hang, Like a loose billet. But on pack horses where that ring doesn't exist or is hard to reach under the pack, I just loop the hobbles around the horses neck like a dog collar. That way, every horse has it's own hobble and I'm not looking for one when it's time to stop for lunch
I coil the lead rope, wrap the snap end around and through, take a short nylon dog collar to wrap around the lead rope as many times as I need to, to make it nice and tight so the snap won't bounce around. Then I fasten the buckle on the dog collar, clip the lead rope snap to the dog collar d-ring and use the trigger snap on my endurance saddle to snap onto either the D ring of the dog collar or the ring of the lead rope. It never comes undone....it stays where I put it and it doesn't bounce around. I love dog collars for inexpensive tie-ons.