This is what I mean. I use 45 feet ('cause my hands are kind of small, my cowboy is using 60 feet) of a pretty soft ranch rope. The coils are stacked in my hand so they come out of it one at a time and from right to left. (I always wear leather gloves except this day I dropped the left one on the way out to the barn and couldn't find it. But when I got home it was on the back step thanks to some kind collie who hadn't even chewed it)
This is what's in my other hand when I'm ready to rope. Note the plaid, LindaG. (Her and I have a plaid thing). The length between the hondu and my hand is called the spoke of the rope and I tend to choke up on mine which means it's a little shorter than what a most good ropers use.
My rope hangs from my saddle when I'm not using it. I have what is called an Oregon Crossover system for tying mine on, which I don't like by the way. I think it's dangerous besides it's always such a big production to take down and tie the rope back on but it does hold it securely so it doesn't come off and maybe get lost when you have to ride hard and fast. I have to wrap the leather around my rope 2 or 3 times then around my horn once.
Then buckle it off to left side. Those bumps are called buck rolls but that's a whole other story.